Posted by: catindiaonline | September 12, 2008

CAT Notes by IIM Topper (part III)

  1. In a direct election between 2 contestants for the post of secretary , 4% of the total votes cast are declared to b illegal. one of the contestants secures 55% of the valid votes and wins with a majority of 240 votes. Find the total number of votes cast.
    2. 2 nos. are greater than the 3rd number no. by 25% and 20% respectively. What % of first number is the 2nd no.?
    3. The no. of boys and girls who appeared at an examination were 16:9 and the no. of boys and girls passing the examination were in the ratio 4:3 . if 75% of the girls passed the exam , find the % of boys who passed the examination and the % of all candidates passing the candidates.
    4. Entry fee in an examination was Re. 1 . later this was reduced by 25% which increased the sale by 20% Find the % increase in the number of visitors.
    5. 2 candidates contested in an election . At the election 10% of the ppl on the voting list did not vote, and 60 votes recorded were rejected as illegal. The majority of the successful candidates was 308 and it was found that he had been supported by 47% of the whole no. on the voters list . what was the number of legal votes recorded by each candidate?
    6. In an examination paper of 5 questions , 5 % of the candidates answered all of them and 5% none. Of the rest , 25% answered only 1 question and 20% answered 4. If 24.5% of the entire number answered only 2questions and 200 candidates answered only 3 questions , how many competed?
    7. The total population of a country is 2.94*10^6 out of which 1.50 million are male and the rest females. Out of every 1000males, 98 can read and write , but only 5.3% of total population can do so. Find what % of women in the whole women population of the country can read and write.
    8. A mans taxable income is Rs 28600. In a certain year the income tax for taxable income over Rs. Rs. 25000 but not exceeding Rs. 30000 is computed according to the following rule- “Total Income Tax = tax – surcharge where surcharge =15% of the tax and tax = Rs. 3200+30% of the amount by which taxable income exceeds Rs. 25000.” Determine the tax he must pay.

    Answers.
    1. 2500
    2. 96%
    3. 56.25%,63%
    4. 60%
    5. 2914,2606
    6. 800
    7. 0.6215%
    8. 4922

SIMPLE INTEREST AND COMPOUND INTEREST.

Here’s a table for calculating SI and CI
—————— S.I. ————- C.I.
1——————–S ————-Upto S
2——————2S————— Upto 2S+X
3————- —–3S————— Upto 3S+3X+
4——————–4S ———— Upto 4S=6X++
5——————–5S ———— Upto 5S+10X+++
6——————-6S ———— Upto 6S+15X+++

“++” it roughly takes a value of Rs. 2 for Rs 100 of X.

Q. the difference between CI and SI is Rs 9848 at 8% interest put out for 4 yrs. What ids the principle?

Method-
For 4 yrs. The value that corresponds is 6X++
So 6X++ = 9848
Here we divide the amt. by 100 and ignore the decimal part so we get 98 and now we subtract 2 from it and now we get 96
So 6x =96 , x =16
8% of SI= 16
So 1% of SI = Rs. 2.
100% of SI =200
200 is 8 % of principle therefore the principle is 2500.
————————————————————————————————————
Sample- What is the interest on Rs. 17250 for 3 yrs. At8% interest compounded annually?

Method- 8*3= 24
(8* Cool/100= 0.64.
0.64*3= 1.92+ (approx. 2)
so 24+2=26%
26% of 17250= 4490
( here all the calculations can be done mentally and approximated, we generally do not need to write. This saves time. And we always have ans. options in the exam, so we can get the ans. closest to it, put we need practice for this)
————————————————————————————————————
Note – For 10% CI it keeps on increasing in this order every year.

1st year 110
2nd year 121
3rd year 133.1
4th year 146.4 and so on.
INSTALLMENT-
Q. A television worth Rs. 15000/- is bought at 10% interest, to be payable in 4 yrs. Tell me the equal installments?

Method –
According to the above table 4 yrs corresponds to 46.4%
So 15000+46.4%= 21960.

Now
1——————–2—————————- 3—————————-4
x——————————————————————————1.331x
——————-x———————————————————–1.21x
—————————————————-x—————————-1.10x

———————————————————————————–4.641x
add all the three to get 4.641

now 4.641x = 21960 so we can find out X.
—————————————————————————————————
MONTHLY INSTALLMENT.

R%= (24*I*100)/N(F+L)
Here I = interest rate
N=no. of installments
F=principle to be paid at time of 1st installment.
L= principle to be paid at time of last. Installment; it can be negative also.
Q. I borrow Rs 500, and pay Rs. 50 monthly for a year find the rate %?
Method- R= (24*100*100)/12(500-50) =44%
Here I comes as 100 coz we pay 50 for 12 months which comes as 600 so 100 is the interest amount.
And L comes as 50 because we have paid 50*11= 550 by now and only Rs. 50 is left over.

—————————————————————————————————
Note–C.I moves in GP and SI moves in AP
0———– 5————-10—————15————20
S.I x———– 1.5x———-2x——- 2.5x—————–3x
C.I x———– 1.5x———2.25x——-3.375x————-5x

At the same intervals previous sum is multiplied by same ratio.
0—————–5———–10————15——————20
CI x————nx———-(n^2)x———-(n^3)x———– (n^4)x

Q. if Rs 5000 becomes Rs 20000 in 10 years. What was the amount after 7.5 years.

Here we take the above table as 0. , 2.5, 5, 7.5, 10. and x, nx, (n^2)x…….
So for 7.5 years. We have (n^4)x =4x
So n^4= 4
N= 2^1/2
( 2^1/2)^3= x
1.414*2.=2.282
2.282* 50000 is the ans.

Note- here i had some problems for formatting the table so u all can see so many” ———————“

  1. A working man has a rise of a 12.5% in his wages rate per hour. There is a drop of 8%in the number of hours worked per week. If his original weekly wages for a week of 50 hrs. was Rs. 120, find (a) his new wages per hour. (b) the percentage increase in the total weekly wages.
    2. A student was asked to divide 7.5 by 8.3 and to obtain the quotient correct to 3 decimal places , but he divided 8.3by 7.5 and got the result correct to 2 decimal places . by how much % was the result wrong?
    3. The incomes of A and B are in the ratio 5:3, their expenses are in the ratio 2:1> if the total annual savings of A and B are 3600 each, find the monthly income of A and B.
    4. The measure of one side of a rectangle is too long by 4% of its true length and that of the other is short by 5% of its true length. Find the error % in measure obtained for the area of the rectangle.
    5. The freight of a machine amounts to 20% of its price. Had the price been 10% less than what it is, the total cost of the machine would have been Rs. 480 less. What is the price of the machine?
    6. Which bargain is better discount: discount series of 20%, 15% and 10% or discount series of 25%, 12% and 8%.

    Answers.
    1. Rs. 2.7/hr, 3.5%
    2. 22.8%
    3. 1500,900
    4. 1.2%
    5. 4000
    6. 2nd

  1. A mixture of 70 lts. Of wine and water contains 10% of water. How much water must be added to make 37% of the resulting mixture?
    2. In what ratio should water be added to a liquid costing Rs. 12 per litre so as to make a profit of 25% by selling the diluted liquid at Rs. 13.75 per litre.?
    3. A man invested Rs. 11000 partly in 6% stock at 125 and partly in 5% stock at 120. The total annual dividend received by him was Rs. 490. Find the amount invested in 5% stock.
    4. The average salary per head of all workers in a workshop is Rs. 95. The average salary of 15 officers is 525 and the average salary of the rest is Rs. 85 . Find the number of workers in the workshop.
    5. A mixture contains wine and water in the ratio 3:2. another contains wine and water in the ratio 4:5 . how many gallons of the latter must be mixed with 3 gallons of the former so that the resulting mixture may contain equal quantities of wine and water?
    6. A cup of milk contains 3 parts of pure milk and 1 part of water. How much of the mixture must be withdrawn and water substituted in order that the resulting mixture may be half milk and half water?
    7. 2 bottles A and B contain diluted sulphuric acid . in the bottle A, the amount of water is double the amount of acid while in the bottle B, the amount of acid is three times that of water. How much should be taken from each bottle in order to prepare 5 litres of mixture containing equal amounts of acid and water?
    8. 2 vessels contain milk and water respectively in the ratio 3:1 and 5:3. find the ratio in which these two are mixed to get a new mixture in which the ratio of milk to water 2:1
    9. One alloy of metal contains 90% copper and 10% tin. Another alloy contains 93% copper 4% tin. If they are mixed so that mixture may contain 9% tin, what % of copper it will contain?
    10. 9 litres are drawn from a cask full of wine and it is then filled with water. 9 litres of the mixture are drawn and the cask is again filled with water. The quantity of wine now left in the cask is to that of water in it as 16:9. How much does the cask hold?

    Answers.
    1. 30 lts.
    2. 11:1
    3. Rs. 6000
    4. 645
    5. 5.4 gallons
    6. 1/3 part.
    7. 3.2
    8. 1:2
    9. 90.5%
    10. 45 lts.

1. Four gallons are drawn from a cask full of wine. It is then filled with water. Four gallons of mixture are again drawn and cask is again filled with water. The quantity of wine now left in the cask is to that of wine in it as 36:13. how much does the cask hold?
2. A vessel contains mixture of spirit and water . spirit is 18%. 8 lts. Of mixture is taken out of the vessel which is again filled with water. If the present percentage of spirit is 15%, find the quantity in lts of the mixture in the vessel.
3. Gold is 19 times as heavy as water and copper 9 times. In what ratio should these metals be mixed that the mixture may be 15 times as heavy as water?
4. AA man buys milk at 85 paise per lt. and mixes water in it. He sells the mixture at the same rate and thus gains 11 1/9. Find the quantity of water mixed by him.
5. @ liquids are mixed in the ratio 5:3 and by selling the mixture at Rs 12.25/ litre, a profit of 16 2/3% is made. If the first liquid costs Rs 4/litre more than the second, find the price per litre of each liquid.

Answers.
1. 28 gallons
2. 48
3. 3:2
4. 1/9 per litre.
5. 1st Rs. 12/.litre, 2ndRrs. 8/litre

  1. Walking at a 4kmph, a clerk reaches his office 5 minutes late. If he walks at 5 kmph, he will be 2.5 minutes early. Find the distance of his office from his house.
    2. A man traveled a distance of 61 kms in 9 hr. partly on foot at the rate of 4kmph and partly on bicycle at the rate of 9kms per hour. Find the distance traveled on foot.
    3. A person has to reach a place 40 kms away. He walks at the rate of 4kmph for the 1st 16 kms. and then travels in a tonga for the rest of the journey. However, if he had traveled by tonga for the 16 kms and covered the remaining distance on foot at 4kmph, he would have taken an hour longer to complete the journey. Find the peed of the tonga.
    4. I traveled 1/3rd of a journey with a speed of 10 kmph , the next one-third with a speed of 9kmph and the rest at a speed of 8kmph. If I had traveled half the journey at a speed of 10kmph and the other half with a speed of 8kmph, I would have been half a minute longer on the way. What distance did I travel?
    5. Two places P and Q are 162 kms apart. A train leaves P for Q and at the same time another train leaves Q for P . The two trains meet at the end of 6 hrs. . if the train traveling from P to Q travels 8 kms an hour faster than the other, find the speed of the 2 trains.
    6. A train 100 mts long meets a man going in opposite direction @5 kmph and passes him in 7.2 seconds . At what rate is the train going?
    7. A train 300 mts. Long overtook a man walking along the line ( In the same direction as the train) at the rate of 4km an hour and passed him in 30 sec. The train reached the station in 15 minutes after it had passed the man. In what time did man reach the station?
    8. A train of 24 carriages, each of 60 mts. Length with an engine of 60 mts length is running at a speed of 60 kmph. Find out the time within which the train will cross the bridge measuring 1.5 km in length.
    9. A train running between two towns arrives at a destination 10 minutes late when it goes 60 kmph and 16 minutes late when it goes 40kmph. Determine the distance between the two towns.
    10. A train traveling @ 60kmph, while inside a tunnel, meets another train of half its length traveling in the opposite direction at 90kmph and passes completely in 4.5 seconds. Find the length of the tunnel, if the first train passes completely through it in 4 minutes 37.5 seconds.

    Answers.
    1. 5/2 kms
    2. 16 kms
    3. 8 kmph
    4. 18 kms
    5. 17.5 kmph, 9.5 kmph
    6. 45 kmph
    7. 2.5 hr.
    8. 3 minutes
    9. 12 kms
    10. 4.5 km

1. A train 150 meters long, traveling at 75 kmph overtakes another train travelling in the same direction at 45 kmph. In how many seconds does the first train pass a passenger sitting in the second train? If the first train passes the second completely in 30 seconds, find the length of the second train.
2. A train going @72kmph over takes another train 192 mts. Long, going in the same direction on a parallel line at 54 kmph and completely passes it in 1.5 minutes. Find the time in which the trains would have completely passed each other, if they had been going in opposite direction, and also the length of the faster train.
3. A boat’s man takes his boat in a river against the stream from a place A to place B where AB=21 km and again returns to A. Thus, he takes 10 hr. in all. The time taken by him down stream in going 7 km is equal to the time taken by him against stream in going 3 km. Find the velocity of the river.
4. Two men together start on a journey in the same direction. They travel 9 and 15 km respectively daily. After travelling for 6 days the man travelling at 9 km per day doubles his speed and both of them finish the distance in the same time. Find the time taken by them to reach their destination.
5. The driver of a car driving at the speed of 38 kmph locates a bus 40 mts ahead of him. After 20 seconds , the bus is 60 m behind. Find the speed of the bus.
6. A monkey climbing up a greased pole ascends 12 mts. And slips down 5 mts. In alternate minutes. If the pole is 63 mts high, how long will it take for him to reach the top?
7. A hare sees a dog 100mts away from her and scuds off in the opposite direction at a speed of 12 kmph. A minute later the dog perceives her and gives chase @ 16kmph. How soon will the dog overtake the hare, and at what distance from the sot where the hare took flight?
8. If one walks @ 5kmph the distance from F.C road to M. G road one would be late for a matinee show by 15 minutes. If one travels by auto rickshaw at 20 kmph one would be early by ½ and hour. How far is M.G road from F.C road?
9. A wire 1mm in diameter can be drawn out from a 14 cm bar of gold in 7 minutes. A wire 0.5 mm can be drawn out from a 20 cm bar of gold in 5 minutes. In how much time will the gold bars be of equal length?
10. A man leaves Bombay at 2.20 pm and reaches Lonavala at 4.10 p.m Another man leaves lonavala at 2.40 p.m and reaches Bombay at 4.52 p.m. When do they pass one another? Give your answer to the closest one minute.

Answers
1. 18 sec,100 mts.
2. 258 mts, 12 6/7 sec.
3. 2 kmph
4. 18 days
5. 20 kmph
6. 16 minutes 35 sec.
7. 4.5 minutes 1.1 m
8. 5 kms
9. 3 minutes
10. 3.29 pm

1. A man goes from Delhi to the village Chhappanpanjeri travelling 300 km by air, 60 km by rail, and 30 km by tonga taking altogether 3.5 hrs. his speed by air is ten times his speed by rail and the speed by rail is 4 times that by tonga. What is his speed by air?
2. A car after traveling for 25 km from a city increases its speed by one fourth its original speed and reaches his destination 40 minutes 40 minutes early. Had it increased its speed 10 km before, it would have reached its destination 5 minutes earlier. What is the distance traveled by the car?
3. A man started from his house to his workplace 8 km away @4kmph so as to reach just in time. After 5 minutes he realized that he had left some important documents at home, so he turned back, and now walking at an increased speed, still succeeded in reaching his workplace in time. What was his speed increased speed?
4. Dinky is picked up by his father by car from school everyday and they reach home at 5:00 pm. One day since school got over an hour earlier than usual, he started walking towards home at 3kmph. He met his father on the way and they reached home 15 minutes earlier than usual time, what is the speed of the car?
5. A train after travelling for a certain distance develops a snag and decreases its speed to half its original speed and reaches his destination 45 minutes late. Had the snag occurred 30 km further on, it would have reached its destination 15 minutes earlier. What is the speed of the train?

Answers.
1. 600 kmph
2. 195 km
3. 4 8/23 kmph
4. 21 kmph
5. 120 kmph

  1. In 1760 meter race, A can beat B by 44 mts. while in a 1320 mts race, B can beat C by 30 mts. By what distance will A beat C in a 880 mts. Race?
    2. A and B run a race. A gives B a start of 55 m and still beats him by 15 seconds. If A runs at 14.08 kmph, find B’s rate in kmph.
    3. Ina km race , If A gives B 40mts start , A wins by 19 seconds, but if A gives B 30 seconds start , B wins by 40 m. Find the time that each takes to run a km.
    4. At a game of chess Mohan can give Ramesh 20 points in 100 and Ramesh can give Dinesh 20 points in 100. How many points can Mohan give dinesh in a game of 100?
    5. Three men A,B and C go around a circle 1760 mts in circumference at the rates of 160, 120 and 105 mts per minute respectively. If they all start together , when will they be together, when they 1st be together again?

    Answers.
    1. 41.5 mts.
    2. 13 1/5 kmph
    3. A =125 secs, B 150 secs.
    4. 36 points
    5. 5 hrs 52 minutes.

  1. At what time between 4 and 5 will the hands of watch:
    i. Coincide?
    ii. Be at right angles?
    iii. Points in opposite directions?
    iv. The minute hand be 13 minute spaces behind the hour hand.
    v. The minute hand be 13 minute spaces ahead of hour hand?
    vi. The two hands will be equidistant from the figure 5?

    2. If the hands of a clock a coincide every every 66 minutes ( true time) how much does the clock gain or lose every hours?
    3. Two clocks are set correctly at 10:00 a.m. on Friday. The first clock gains 2 minutes per hour and gains twice as much as the second. What time will the second clock register when the correct time is 2 p.m on the following Monday?
    4. My watch, which gains uniformly, is 2 min. slow at noon on Saturday, and is 4 minutes 48 seconds fast at 12 p.m. on the following Sunday. When was it correct?

    Answers-
    I. 21 9/11 minutes past 4
    II. at 5 5/11 min. past 4 and again at 38 2/11 past.
    III. 54 6/11 minute past 4
    IV. 7 7/11 past 4
    V. 36 minutes past 4
    VI. 27 9/13 min. past 4

    1. gave above
    2. 60/121
    3. 3 hours 16 minutes
    4. the watch was correct at 12 pm on Monday.

1. Which is a better investment? 35 stock at 86or 4% stock at Rs. 110.
2. A man invests equal sums in 3% stock at 80 and 5% stock at 120. If the total yearly income from both the stocks is Rs. 380, find his investment in each stock.
3. A man transfers his sock of Rs. 7600 from 5% at 105 to 45%. Thus he loses Rs. 2. find the market value of the other stock.
4. A man receives Rs. 10825.12 in a year as dividend and interest. He received dividend at the rate of 9.6% which is equal to 75% of his income. He got average interest on his saving at 6.4% which is equal to rest of the part of his income. Find his investment purchasing stock and his saving.
5. A company gives 8% dividend. Mohan has 500 shares each of face value Rs. 10 of this company. He sells these shares at 605 premium and purchases shares each of face value Rs. 5 of another company which are being sold at 20% discount. If the other company gives 5% dividend, then find the difference of his gains from the dividends.
6. A man transfers his stock from 3.5% at 63 1/8 to the 5% at 74 7/8. brokerage 1/8% is allowed on each transaction and thereby increases his annual income by Rs. 21. Find the original stock held by him.
7. Divide Rs. 5300 in two parts such that if one parts such that if one part is invested in the 3.5% at 98 and other in 4% at par, the resulting incomes are equal.
8. A man invests Rs. 2490. He puts in Rs. 900 in 3.5% stock at 75 Rs. 850 in 3% at 68 and the remainder in 6% stock. Total yield from his investment is 5%. At what price does he buy 6% stock?

Answers.
1. Rs.3.5 approx, Rs 3.6 approx
It is more advantageous to invest money in the second stock.

2. Rs. 4800
3. Rs.95
4. Rs 84571.25, Rs.42285.62
5. Rs 100
6. Rs 3000
7. Rs. 2800, Rs. 2500
8. 98 2/3

. The sum of 7 nos. is 235. the average of 1st three nos. is 23 and the average of last three is 42. find the 4th number.
3. A man purchased 5 cows@ Rs 1500 each. 6 cows @ Rs 2000 each and 9 cows @ rs2500 each. Find the average cost of cows.
4. The average marks of 500 students in an examination are 45. Among them the average marks of the last 150 are 25 and that of the top 150 students are 75. what are the average marks of the remaining 200 students.
5. The average age of 25 boys of a class is 13 yrs. If 5 such students are admitted to this class, whose average age id 14.5 years, then find the average age of total number of boys.
6. The average temperature of Monday, Tuesday and Wednesday was 60 degrees. The average temperature of Tuesday, Wednesday and Thursday was 65 degree The temperature of Thursday was 62 degrees. Find the temperature on Monday.
7. The average temp of Monday, Tuesday, Thursday and Wednesday is 62 degrees. The average temperature of Monday and Tuesday is 56 degrees. The ratio of temperature of Wednesday and Thursday is 15:19. find the temp of Wednesday and Thursday.
8. The average weight of 4 persons A, B,C and D is 67 kgs. When the 5th man E joins them , the average weight is reduced by 2kgs. A is then replaced by another Man F , whose weight is 4 kg more than E’s and consequently the average weight comes down to 64 kg. find the weight of A.
9. A bats man has a certain average runs for 16 innings. In the 17th inning , he made a score of 87 runs thereby increasing his average by 3. what is his average after 17th inning?
10. Ina cricket match, 6 players had a certain average of their runs. 7th player makes a score of 112 runs, thereby increasing the average of their runs by 10. find the average after of the 1st 6 players.

Answers.
1. 65
2. 40
3. Rs. 2100
4. 37.5
5. 13.25 yrs
6. 47 degrees
7. 60,70 degrees
8. 66kg
9. 39
10. 42

  1. In a class of boys and girls, the average age of 40 boys is 13.5 years and that of girls is 13 years. The average age of whole class is 13.4 years. Find the number of girls in the class.
    2. The average weight of boys in a class is 43 kg. later four boys, whose weights are respectively 42 kg, 36.5 kg, 39 kg and 42.5 kg. the average now becomes 42.5 kg. Find the original number of boys in the class.
    3. The average age of 8 men increases by 2 years when two women are included in a place of two men of ages 20 years and 24 years. Find the average age of the women.
    4. The average salary per head of the entire staff of an office including the officers and clerks is Rs. 90. The average salary of the officers is Rs. 600 and that of the clerks is Rs. 84. If the number of officers is 12, find the no. of clerks in the office.
    5. A man had 7 children. When their average age was 12 years, the child who was 6 years of age, died. What was the average of the surviving children 5 years after the death of his child?
    6. Of the three number the 1st is twice the second and the second is twice the third. The average of 3 nos. is 35. find the numbers.
    7. In each row of a hand written book of 180 pages, there are 12 words on a n average and each page consists of 16 rows on a n average. After printing, in each row of the book these are 18 words on average and each page contains 20 rows on an average. Find the number of pages of the printed books,
    8. Visitors to a show were charged Rs 15 each on the 1st day, Rs. 7.5 on the 2nd , Rs 2.5 on the 3rd and the total attendance of 3 days were in the ratio 2:5:13 respectively. Find the average charge per person for the whole show.

. 9. A table is made of mean monthly temperature for the first six months in a year. The temperature of January is 8/9 that of April, that of February is 11/0 of January, of march is the same as that of February. The average temperature of April and june is 4 degrees more than the average temperature of all six months. The average temperature of march and may is equal to the average temperature of 6 months. The average temperature of January and May is equal to the temperature of march. The temperature of may is 48 degrees. Find the average temperature of 6 months and the temperature of June.
10. A ship, 40 km from shore, springs a leak which admits 3 ¾ tones of water in 12 minutes. 60 tonnes would suffice to sink her, but the ship’s pumps can throw out 12 tonnes of water in one hour. Find the average rate of sailing, so that she may reach the shore just she begins to sink.

Answers.
1. 10
2. 20
3. 30yrs
4. 1020
5. 18 yrs.
6. 15.30.60
7. 96pages
8. Rs. 5
9. 46 degrees ,55 degrees
10. 4.5 kmph

  1. A alone can do a piece of work in 6 days and B alone can do it in 8 days. How long would it take for A and B to finish the work?
    2. Mohan can do ½ of a work in 8 days while Sohan can do 1/3 of the same work in 6 days. How long would it take for Mohan and Sohan to finish the work?
    3. A can do apiece of work in 45 days. He works at it for 5 days and then B completes it in 20 days. How long will A and B together take to complete the work?
    4. Mohan does a work in 12 days and Sohan does the same work in 20 days. Mohan alone started the work and after 4 days, sohan began to do work with Mohan. Find

    I. How much work did Mohan do in 4 days?
    II. The balance work
    III. In how many days did both together finish the balance work?

    5. Ram finished 3/5 of a work in 9 days and the remaining work he finished in 4 days with the assistance of Shyam. Find in how many days Shyam alone can finish that work?
    6. A can do a piece of work in 120 days and B can do it in 150 days. They work together for 20 days. Then B leaves and A continues the work alone, 12 days after C joins A and the work is completed in 48 days more. In how many days can C do it if he works alone?
    7. A and B can do a piece of work in 12 days, B and C together do it in 15 days. If A is twice as good a workman as C, find in what time B alone will do it?
    8. A and b could do a piece of work in 40 days; after working for 10 days they are assisted by C, and the work is finished in 20 days nore. If C does as much work in 2 days s B does in 3 days, in how many days could each of them do the same work alone?
    9. 3 taps empty a cistern in 3 hrs. First tap alone can empty it in 6 hrs. and second tap alone can empty it in 9 hrs.. How many hours would third tap alone take to empty the cistern?
    10. Two pipes A and B would fill a cistern in 37.5 minutes and 36 minutes respectively. Both pipes being opened, find when the 2nd pipe must be turned off, so that the cistern may be filled in half an hour?

    Answers-
    1. 24/7 days
    2. 8 8/17 days
    3. 15 days
    4. ..
    I. 1/3
    II. 2/3
    III. 5 days

    5. 30 days
    6. 240 days
    7. 20 days
    8. C= 80 days, B =`120 days, A =60 days.
    9. 18 hrs
    10. after 9 minutes

  1. A pipe can fill a bath in 20 minutes and another can fill it in 30 minutes. A person opens both the pipes simultaneously. When the bath should have been full, he finds that the waste pipe was open. He then closes the waste pipe and in 3 minutes more, the bath is full. In what time, would the waste pipe empty it?
    2. A,B,C are employed to do a piece of work for Rs 529. A and B together are supposed to do 19/23 of the work and B and C together 8/23 of the work. What should A be paid?
    3. A contractor receives every week a certain sum which he uses for paying wages. His capital together with weekly subsidy, would just enable him to pay 42 men for 52 weeks. If he had 60 men at the same wages, his capital together with the weekly subsidy , would just suffice for 13 weeks. How many man can be maintained for 26 weeks?
    4. 2 taps can separately fill a cistern when the waste pipe is closed in 10 and 12 minutes respectively and when the waste pipe is open they together fill it in 15 minutes. How long does it take the waste pipe to empty the cistern, when the taps are closed.
    5. A cistern can be filled by one of the two pipes in 30 minutes and the other in 36 minutes. Both pipes are opened for a certain time but being partially clogged, only 5/6 of the full quantity of water flows through the former and only 9/10 through the later. The obstructions, however, being suddenly removed, the cistern is filled in 15.5 minutes from that moment. How long was it before the full flow of water began?
    6. A supply of water lasts for 200 days if 10 gallons leak off everyday, but only for 180 days if 16 gallons leak off daily. Find the total quantity of water in the supply.

    Answers.
    1. 48 minutes
    2. Rs. 345
    3. 48 men
    4. 8 minutes 34 secs.
    5. 1 minute
    6. 9 minutes

  1. The C. P. of 12 pens is equal to S.P 0f 10 pens, find the gain %.
    2. In selling an article for Rs. 9, a man gets as much percent loss as is the prime cost?(C.P) of that article. Find the C.P. of that article.
    3. A person purchases 50 dozen eggs at Rs. 4 per dozen. Of these , 40 eggs were found broken. At what price should he sell the remaining eggs in order to make a profit of 5%?
    4. A man purchases 216 eggs @Rs 2 per dozen. Few of these r broken. The remaining eggs, he sell @Rs 2.28 per dozen. If he gets 20% profit, find the no. of broken eggs.
    5. A merchant sold two radios for 120 each. One was sold at a loss of 25% of the cost and other was sold at a gain of 25% of the cost. Determine the total amount of gain/loss in the entire transaction.
    6. A person purchases 90 clocks and sells 40 clocks at a gain of 10% and 50 clocks at a gain of 20%. Had he sold all of them at a uniform profit of 15%, he would have got Rs 40 less. Find the C.P. of each clock.
    7. a man purchases some oranges @3 for Rs 4 and same quantity 2 5 for Rs 6. If he sells all the oranges @ 3 for Rs 5, find his gain or loss%.
    8. A man sells 2 cars for Rs 19,550 each. On one he gains 15% and on the other he losses 15%. Find his total gain or loss and also his gain or loss%.
    9. A merchant buys 40 bicycles and marks them at 25% above C.P. He allows a discount on the marked price at 10% for cash sales, and at 5% for credit sales. If 3/4th of the stock is sold for cash and the rest for credit, and if the total profit be Rs. 2025, what is the C.P of the Bicycle?
    10. The catalogue price of a radio is Rs. 720. If it is sold at a discount of 16 2/3% of the catalogue price, the gain is 25%. If it is sold for Rs. 160 below the catalogue price, find the gain or loss%

    Answers.
    1. 20%
    2. Rs 90 or Rs.10
    3. Rs 4.50/dz
    4. 36
    5. Rs.16
    6. Rs 80
    7. profit =Rs.31, 11/19%
    8. Rs. 900, 2 ¼%
    9. Rs. 360
    10. 16 2/3% gain

  1. If price of sugar falls by 12.5% a person can buy 9 kg more of sugar for Rs 126 than before. If the price had risen by 12.5%, how much sugar would he have bought for the same sum?
    2. A tradesman defrauds by means of a false balance to extent of 10% in buying goods and to the same extent in selling goods. What % does he gain or loose on his outlay by defraud?
    3. A merchant sells 90 quintals of wheat at a profit of 8% and 50 quintals at a profit of 10%. If he had sold the whole at a profit of 9%, he would have received Rs 60 more than he actually did. How much did the merchant pay for the wheat per quintal?
    4. A tradesman sells one kind of sugar at Rs 3 per Kg. and looses 20% and another kind of sugar @ Rs 5 per Kg. He mixes the two together in equal proportion and sells the mixture at Rs 6/kg. what is now the gain%?
    5. A publisher printed 2000 copies of a book at a cost of Rs 2400. He gave 500 copies free to the head of the institutions. He allowed a discount of 25% on the published price and gave one extra copy for every 24 copies bought at a time. He sold all the copies in that manner. If the published price is Rs 3.25, find his gain or loss%.
    6. A man purchases 5 horses and 10 cows for Rs 1000. He sells the horses at 15% profit and the cows at 10% loss. Thus he gets Rs. 375 as profit. Find the cost of 1 horse and I cow separately.
    7. A man buys goods and finds that cost of carriage is 4% of the cost of goods. He is compelled to sell at a loss of 5% on his total outlay, if however , he had received Rs 32.50 more than he did, he would have gained 2.5%. What was the original cost of the goods?

8. A manufacturer fixes the wholesale price of an article by adding together the cost of production, excise duty( which is22% of the cost of production) and his profit (which is 18% of the cost of production). The wholesaler sells the articles to a retailer at a profit of 15%. The retailer marks the price at 25% above his cost price and allows 4% discount on the marked price of cash payment. Find the production cost of the article for which a customer makes a cash payment of Rs. 483 to the dealer.
9. A manufacturer fixes the wholesale price of an electric appliance by adding cost of production, excise duty(which is 30% of the production cost) and profit (which is 20% of the production cost). The wholesaler sells the appliances to a retailer at a profit of 20%. The retailer in turn, sells the item to a customer for Rs 207, thereby earning a profit of 15%. Find the production cost and the excise duty on the appliance.
10. An almirah is listed at Rs 1000. A retailer buys it with 2 successive discounts of 10% and 20% for cash . the other expenses are 10% of cost of the almirah. At what price should he sell to earn a profit of 15%?
11. A pen is listed for Rs 12. originally a 15% discount was allowed. Later the wholesaler gave a 2nd discount thus bringing the net price down to Rs. 8.16. find the 2nd discount %.

12. At the off season period a hotel offers a double bed room at a discount of 30%. If there is a successive discount of 10% to tourists in groups, a double bed room becomes available for Rs 189 per day .find the original room rent.
13. A tradesman fixes the sale price of his articles 30% more than the C.P.. Half of the articles , he sells at this increased sale price and ¼ portion , he sells at 15% discount of this sale price. And the remaining , he sells at 30% discount of this sale price . what % profit did occur to the tradesman?
14. The purchase tax on an article is levied at the rate of 66 2/3 % of its wholesale price, while the retailer’s profit amounts to 20% of the retail price of the article. Find the wholesale price of an article which is retailed at Rs 12.50
15. Two dealer offer an article at the same list price. The first allows a discount of 25% and offers further a rebate of 15% on the discounted price for cash payment. The other dealer offers a discount of 10% and allows a further concession of 30% on the discounted price of cash payment. What is the better offer to the buyer?
16. A bicycle costs Rs 260(including 4% sales tax) payable in 60 days. A discount of 6% on the selling price (excluding the sales tax) is given by the shopkeeper to a customer who makes cash payment on the spot. If a customer pays in 60 days, how much interest per annum is he paying on the transaction?
17. If a dealer were to diminish the selling price of his wares by 10% and thereby doubled his sale, he could make the same profit on the cost price as before. In what ratio would his profit be diminished if he were to increase the selling price by the same amount and thereby halve his sale.
18. At a cricket match , the contractor provided dinner for 24 persons, and fixed the price so as to gain 12.5% upon his total outlay. Three of the players being absent , the remaining 21 paid the fixed price for their dinner, and such the contractor lost one rupee. What was the charge for the dinner?
19. A family buys farm equipment with a list price of Rs.2114.75. The salesman tells them that he will sell it to them for Rs.1950 if they pay the full amount in cash. What % discount would they be getting?

Answers.
1. 56 kg
2. 22 2/9%
3. Rs. 150/qntt.
4. 54 26/31%
5. gain 46 ¼%
6. Rs 1100, Rs 450
7. Rs. 416.66
8. Rs 250
9. Rs.100 Rs. 30
10. Rs 910.80
11. 20%
12. Rs.300
13. 15 3/8%
14. Rs. 6
15. second one
16. Rs.90
17. 4:3
18. Rs.3
19. 7^6687/8459%

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