1. If 3:21::a:63, then find the value of a
2. If a:b=8:15,b:c=5:8 and c:d=4:5 find a:d
3. Find the mean proportion to 9 and 4.9
4. Find the third proportional of 6 and 30
5. The ratio between 2 quantities is 5:7, If the first is 155, find the other.
6. the shadow of qutab minar , which is 72 mts. High is 8 mts. At a particular time of day. Find the height of an electric pole which casts a shadow of 10 mts, under the similar conditions on the same day and time.
7. Two car drivers take 3 ¼ hours and 4 hrs. respectively to cover a distance of 650 kms. From a city P to Q. Find the ratio of the average speeds of the two cars.
8. Two numbers bear a ratio of 2:7. If each of them is increased by 14, then their ratio becomes 4:7. find the two nos.
9. Two numbers are in the ratio of 4:7.The difference of their squares is 132. Find the numbers.
10. If 16 men working 7 hrs. a day can plough a field in 48 days, in how many days will 28 boys working 12 hours a day plough the same field, if one man does a work as 2 boys.
Answers.
1. 9
2. a:d=4:15
3. 2.1
4. 150
5. 217
6. 90mts.
7. 16:13
8. 6 and21
9. 8 and14
10. 4 days.
1. A contractor undertook to finish a certain work in 124 days and employed 120 men. After 64 days, he found that he had already done 2/3 of the work. How many men can be discharged now so that the work may finish in time?
2. The length and breadth of a rectangle are increased in the ratio 3:4 and 4:5 respectively. Find the ratio between new ones and old areas.
3. A man went to the market to buy fruits. He bought apples, mangoes and dates. The ratio of the weight of apples to that of mangoes bought is the same as the weight of mangoes to that of dates bought . if ha bought 7.2 kgs of apples and 5 kg of dates, find the weight of mangoes bought.
4. A grey hound pursues a hare and takes 4 leaps for every 5 leaps of the hare; but 3 leaps of the hound are equal to 4 leaps of the hare, compare the rates od the hound and hare.
5. A mixture consists of three substances whose volumes are in the ratio 5:6:8. the weights of equal volumes are in the ratio 4:5:3.what is the ratio of the weight of the three substances composing the mixture?
6. The force of gravity at the surface of a planet is jointly proportional to the density of the planet and its radius. The planet Jupiter has a radius equal to ten times the radius of the earth. The densities o Jupiter and earth are respectively 1.75 and 5.67. if a can jump to a height of 1500 cm, on earth how height can he jump on the surface of Jupiter, given that the height to which a man can jump is inversely proportional to the force of gravity?
7. The distance of the horizon at sea varies as the square root of the height of the eye above the sea level. When the distance is 14.4 kilometers, the height of the eye is 18 mts.. find in kms. the distance when the height of the eye is 8 mts. , and find in mts. The height of the eye when the distance is 7.2 kms.
8. The pressure of a certain mass of a gas varies inversely as its volume. When p(measured in kg. weight per square decimeter) is 20 then v( measured in cubic decimeter) is 450. find in kg. weight per square decimeter the pressure when the volume is 300 cubic decimetres. Also find volume when the pressure is 60 kg weight per square decimeter.
Answers.
1. 56 men
2. 5:3
3. 6kg.
4. 16:15
5. 10:15:12
6. 486 cm
7. 9.6km, 4.5 m
8. 30,150 

CLOCKS.
• Here “#” means degrees.
• Normal clock has 60 divisions and each division =6 #
• In 60 minutes , minute hand moves 60 divisions whereas hour hand covers 5 divisions whereas hour hand covers 5 divisions, therefore minute hand overtakes 55 divisions in 60 minutes, so to overtake 1 division it needs 12/11 minutes.
• Minute hand covers 12 times the no. of divisions covered by hour hand in same time.
• Whenever u need to imagine; imagine the position of hand at exact hour, because u know the gap between the hour hand and minute hand=( hour*5) and minute hand is behind
• Angle between hands – (11m60h)/2, If the angle calculated does not exists in the ans. options, then subtract your ans. from 360#
• Whatever position comes 1 in an hour, it takes place 11 times in 12 hrs.
• When u get ans. in decimals then remember base is 60.
• For every hour the gap is 60/13
• I f two watches move at different speeds, then they show the same time when the gap is 12hrs. or 720 minutes.
• We use the concept of ratio to find time.
In a normal watch hands coincide every 65 5/11 minutes. If it is written that hands are coinciding every 65 minutes. it means, true time is 65 minutes but watch is giving 65 5/11 minutes, so it is gaining 5/11 minutes every 65 minutes, therefore to calculate the variance , we find the number of time periods of 65 minutes and multiply it by 5/11
Q. when will there be an angle of 30# between 5 and 6?
Method 5*5= 25
30/6= 5, 6 here means 6 divisions.
Now we get 2 answers
i. 255=20 so 20*(12/11)
ii. 25+5=30 so 30*(12/11)
Q. what time between 5 and 6 in a railway clock both hands will be together.
Q. Between 7 and 8 , what time will the minute hand and the hour hand be pointing towards each other.
Q. Between 5 and 6 both the hour hand and the minute hand are equidistant from 5, but they r not together. What is the time?
Q. what is the change in angle from 3:10 to 3:20 pm.?
A train came at 4:15 and left between 4 and 5 and the angle remained same. What is the duration of the halt?
Q. I sent my servant between 3 and 4 and he came back between 4 and 5. hands had interchanged their positions. What time he came back and went out. How much time had the servant gone out?
Q. A watch looses 3 minutes every 2 hrs, it was set at 8:00 am on Sunday. When will it show the same time again.
Q. A watch gains 0.25% in the 1st week then losses 0.5% in the 2nd week. What variance it shows?
Q. In a wall clock, the minute hand is 6 inches long and hour hand is 4 inches long, what is the difference in area swept by both the hands between 2:15 and 4:15?
Q. At 8:00 am on Sunday watch A was behind by 10 minutes and watch B was ahead by 12 minutes. On Monday at 2:00 pm watch A was ahead by 5 minutes and watch B was behind by 6 minutes.
i. When watch A showed the correct time what was the time in watch A.
ii. When watch B showed the correct time what was the time in watch B.
iii. When did watch A and B show the same time?
iv. When watch A and B showed the same time, what was the time in A and B.
Q. A clock takes 6 sec. to strike 6, how much time it will take to strike 12?
 The ratio of milk and water in a 20 lt. mixture is 3:1. how much milk must be added so that this ratio become 4:1
2. Rs. 232 are divided among 480 children such that each boy gets 40 paise and each girl gets 60 paise. How many girls were there?
3. A certain sum of money is distributed among two friends in the ratio 5:11. If one of them got Rs. 1200 more than other, what was the total sum?
4. Divide Rs.395 among A,B,C such that B gets 25% more than A and 20% more than C.
5. Divide Rs. 730 among Sudha ,Kamla, and Kamal such that if Sudha gets Rs. 3, then Kamla gets Rs.4 and if Kamla gets Rs. 3.50, then Kamal gets 3.
6. Divide Rs. 4300 in A,B,C and D such that when A gets Rs. 9, then B gets Rs. 6 then C gets Rs 5 and when C Rs. 4 then D gets Rs. 3.
7. Divide Rs. 558 IN A,B, C such that if Rs. 4,6 and 8 are decreased respectively from their shares then the ratio of their shares is 2:3:7.
8. Divide Rs. 258 in 8 men , 6 women and 10 children such that a woman gets 3/2 of a child and a man gets twice of a woman. What is the share of each man , women and child?
9. Rs. 430 are divided among 45 persons consisting of men women and children. The combined shares of all men , all women and all children are as 12:15:16 whereas the individual share of a man , a woman, and a child are as 6:5:4. find what one man , one woman and one child gets.
10. A bag contains 1 rupee, 50paise and 10 paise coins. The ratio of 1 rupee and 50p coins is 2:5. the ratio of 50p and 10p coins 1s 4:9. If total money is Rs. 1125, find the number of each type of coins.
ANSWERS
1. 5lts.
2. 200
3. 3200
4. Rs 120,150,125.
5. Rs. 210,280,240
6. Rs. 1350,1200,1000,750
7. Rs.94,141,323
8. .Rs.18,9,6
9. Rs 12,10,8
10. 32,80,160.
1. Between 2 stations the first , second and the third classes fare were fixed at first in the ratio of 8:6:3, but afterwards the 1st class fares were reduced by 1/6 and the 2nd class by 1/12. in a year, the number of first, second and third class passengers were respectively 9:12:26 and the money at the booking offices was 1088. How much was paid by first class passengers?
2. If Rs.150 be divided among 6 men, 12 women, and 17 boys so that 2 men receive as much as 5 boys and 2 women as much as 3 boys, how much will each man, woman and boy receive?
3. Annual incomes of A and B are in the ratio 4:3 and their annual expenses bear a ratio of 3:2. If each of them saves Rs. 600 at the end of the year, find the annual income of each.
4. A student appeared in an examination with hindi ,english, physics, chemistry and maths. As subjects. He got the marks in these subjects in the ratio of 5:3:4:6:7. the maximum marks in each subjects were 100. he got 70% marks in aggregate in all subjects. if he gets 60% marks are essential for getting first class in each subjects, then point out the subjects in which he got first division.
5. The annual income of A,B,C taken together is Rs. 33600.A spends 80% of his income , B spends 87.5% of his income and C spends 90% of his income. if their annual savings are as 16:17:12, find the annual saving of each.
6. At the beginning of a term, the ratio of the number of boys in a school under 15 years to those over 15 years age was 5:4. At the end of term the ratio was 7:8 as 20 of the boys had reached the age of 15 during the term. Find the total number of boys in the school , given that no boy left or was admitted during the term.
7. A man gives 3/8 of his property to one son and 30% of the remainder to another . he then distributed the remaining property among three charities in the proportion 2:5:7.The difference of his son’s share is Rs. 1800. what was the value of his property and how much was given to each charity?
Answers.
1. Rs.320.
2. Rs.7.50,4.50,3
3. Rs.2400,1300
4. hindi 70, chem.. 84, maths 98
5. 1600, 1700 1200
6. 225
7. Rs.600,1500,2100 

1. It was intended that Rs. 19.50 should be divided between three boys A, B,C, in the ratio of 2:3:4 but by mistake the distribution was made in the proportion of 1/2: 1/3:1/4. how much does B gain or loose by error?
2. Three persons A,B and C agree to pay their total bill in the proportion 4:5:6. a pays the first day’s bill which amounts to Rs. 45.75;b the second days bill which amounts to 59.60 and C the third day’s bill which amounts to Rs. 74.65. how must they settle their accounts?
3. a employer reduces the number of his employs in the ratio of 9:8 and increases the wages in the ratio of 14:15..Find in what ratio the wage bill is increased or decreased and find the difference in the amount of the bill, if it was previously Rs. 1680.
4. a sum of Rs. 2368 was divided among 8 men, 10 women and 12 children in such a way that each man got 25% more than a woman and each women got 25% more than a child. How much did each woman get?
5. A man , his wife and son worked in a garden . the man for 2 days, his wife for 3.5 days and the boy for 4 days. Their daily wages were, man’s to women’s in the ratio of 7:4 and the man’s to boy in the ratio of 7 to 3. their total earnings amounted to Rs. 60. find the daily wages of each.
6. A tin is full of wine. out of this tin 4 gallons of wine are taken out and 4 gallons of water are added. After this 4 gallons of mixture were taken out and again 4 gallons of water were added. Now ratio of wine and water in the tin 36:13. find the volume of tin?
7. If an election in which each elector may vote for 2 candidates, half of the electors vote for a but divide their other votes between B,C, D in the ratio 3:2:1. of the remainder , half vote for B and divide their votes between C and D, in the ratio of 2:1. Of the remainder, half vote for C and D. and the remainder 840 in number do not vote. How many votes does each candidate get?
Answers.
1. Rs. 0.50 loss
2. A to C Rs. 2.25, B to C Rs. 0.40
3. 21:20,Rs.80
4. Rs.80
5. Rs. 10.50, 6,4.50
6. 28 gallons
7. 3360,3360, 3080, 1960. 

1. The price of cloth is increased by 20% . By how much % must a family reduce the consumption of the cloth so that their expenditure may remain the same.
2. A reduction of 40% in the price eggs would enable a purchaser to purchase 48 more eggs more for Re. 1. Find the reduced price per dozen . Also find the original price.
3. If the price of sugar falls by 12.5%, a person can buy 9 kgs. More sugar for Rs. 126 than before. If the price had risen by 12.5%. How much less sugar could ha have bought for the same sum?
4. A candidate secured 20% marks in an examination and failed by 10 marks . another secured 42% marks and got 1 mark more than the marks required to pass the examination. Determine the maximum number of marks and the % necessary to pass the examination.
5. In an examination 40% marks are required to pass. A obtains `0% less than the no. of marks required to pass. B obtains 11 1/9% less than A, and C 41 3/17% less than the no. of marks obtained by A and B together.Does C pass or fail?
6. In an examination 75% candidates passed in English and 70% candidates passed in maths, 23% candidates failed in both subjects. If 136 candidates passed in both the subjects, find out the no. of candidates that appeared in the examination.
7. The population of a town increases by 10% every year for 2 yrs. And then decreases by 10% every 2 yrs. If the population just before 4 years was 10000, what was it after 4 years.
8. At an election , a candidate secures 40% of the total votes but is defeated by the other candidate by 300 votes. Find out the total number of votes polled.
9. 10%of the soldiers of an army are killed in the battle. 105 of the remaining soldiers died of disease and 10% of the remaining were disabled. Now only 72900 soldiers are left in the army. How many soldiers were there in all in the army in the beginning.
10. Mohan saves 20% of his salary . due to dearness his monthly expenditure increases by 20% and then he is able to save only Rs. 20. find his monthly salary.
Answers.
1. Rs. 16 2/3
2. new 10 ps, price 16 2/3 ps.
3. 7kg
4. 40%
5. pass
6. 200
7. 98010
8. 1500
9. 1000000
10. Rs 500 

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