Posted by: catindiaonline | September 12, 2008

CAT Notes by IIM Topper (part I)

COIN CONCEPT

When 2 quantities are sold as a group together .
Here r some more fundas, with examples.

Example- A horse and a carriage were bought for Rs. 12000. the carriage was sold at a loss of 10% , horse was sold at a profit of 20%. Together I received Rs.13500. what is the C.P. and S.P. of each.

Method-Assume everything to be a horse, so I shud have sold everything at 20% profit.20% of 12000+12000= 14400.But I received Rs. 13500 only that makes a difference of 900 or Rs. 900 are less. This also makes a difference of 30% coz we calculated 40% profit (20+20%), but we had [+20%+(-10%)]=10%
I calculated 30% more on carriage.
30% or carriage=900
therefore 100%=3000
so now we have the individual cost of the horse, the carriage is for 9000/-and the S.P. can b calculated now.

We have similar questions in many forms which can b done by applying the above concept

Sample Question. 5 kg of rice and 2 kg of tea cost Rs/- 35, prices of rice grew by 10% and tea by 35% and together I could purchase it for Rs.420. What is the price of tea.
(in these type of questions, whatever is asked take reverse of that, here tea is asked so work on rice.)

Method
350+10% of 350=385
420-385=35
There is a difference of 25%(35%-10%)
This is Rs. 35
25% corresponds to Rs. 35
therefore 100%=140
2 Kg=Rs 140. so 1kg =70

Example.- I hired a servant for Rs. 300 per month and a cycle if he works for a year. After 8 months I threw him out and paid him Rs. 50 for that month and the cycle. How much does the cycle cost?

Method
– In 8 months the servant has earned 2/3rd (8/12) of the cycle. So he is left with just 1/3rd of the cycle, which we will cut in place of 300 we gave him only 50.
1/3 corresponds to (300-50)=250
therefore 1=750. so the cost of the cycle is Rs. 750.

Sample Questions –

1. Deccan queen moves for Pune from Mumbai at 5:00 a.m. and it reaches Pune at 9:00 a.m. .Shatabdi starts at 7:00a.m. from Pune and reaches Mumbai at 10:30 a.m.. What time did the 2 trains meet.
2. Ajay and Vijay are at a distance of 100 mts., when 3rd time they meet ,they are at a distance of 20mts from Vijay’s side and each of them have completed at least 100 mts., what are the ratio of the speed of Ajay and Vijay.
3. One car sets off at 8:00 a.m. at 60kmph, at 11:00 a.m. another car starts at 100kmph. At what distance from the starting point both will meet.
4. Mumbai to Pune local starts at 5:00 a.m. and they end at 12:00in the night. They take 4 hrs .And every 15 mins. one local is initiated from each station. – a)A 5:00a.m. local will meet how many locals in its journey. b) at what intervals it will meet the local.
5. On a highway12 trucks cross in 1hour at the equal intervals, if I move from opposite directions at double the speed of the truck , in one hr. I will cross how many trucks?
6. Vijay and Pallavi went for 100, mts. ski race. Initially Pallavi’s speed was 1m/smore so Pallavi gave Vijay some lead in terms of time, when Pallavi caught up with Vijay, then Vijay increased his speed by 2m/s and he was the winner by 7 minutes and 8 seconds. Had the race been 500mts longer, he would have won by 25 more seconds. A) at what point Pallavi caught up with Vijay b.) what was the lead given to Vijay. C)speed of Pallavi, speed of Vijay.

Ans. for each question.
1. 7:56 a.m.
2. ratio-14:11
3. 450kms.
4 a)17 trains
5 36 trucks.
6 A)1440 mts. C)V-3m/s P-4m/s.

7. On a republic a day a 10 KM convoy has to cover 30km distance. Convoy moves at 10kmph. A motorcyclists starts from back of the convoy, moves in front , again goes back and from back again goes to the front, and in the mean time the convoy has completed its journey.
a. What is the speed of the motorcyclists?
b. If he increases his speed by double, then how many rounds will he take ?

8. A,B,C had to go 100 kms. A had a motorcycle by which he could go@25 kmph. Walking is done @5kmph. A picks up B, while C walks, after sometime A drops B , B moves on , A comes back picks up C and all of them reach at the same time.
a. At what distance B was dropped
b. Motorcyclists traveled how many kms?
c. Journey is of how many hours?
d. A picked up C at what distance?

9. Robbery took place at 5:00a.m. and robbers took at speed of 60kmph at 9:00 a.m. police went after the chase @80kmph . A helicopter moved @120 kmph which used to go to the robbers and come back to police and again go back. Ultimately when robbers were caught, helicopter had moved how many kilometers toward the robbers.

Sample questions.

1. A,B,C can finish the work in 10,12,15 days. A,B started working, then B left after 2 days. In how much time the work will be completed, if C joined after 4 days.
2. A can do a work in 15 days, A& B started, but after 4 days B left and the work was completed in 10 days. How much time will B take to complete the whole work.
3. A can finish a work in 30 minutes , B in 45 Minutes, but C was disturbing them and breaking the work ,They could finish the work in 3 hours. How much time c can break the work.
4. ( use data form above question also) If C is a destroyer and talks 10 days to destroy the work and order being A,B, C. In how much time work will be completed.
5. A can do a work in 20 days , B in 10 days and C in 25 days. 1 day before the work was to be completed C left, then half day before the work was scheduled to be completed B left and now A completed the work.
a. In how many days the work will get over?
b. How much extra time was taken?

Re: Important Table


CALENDAR.

1. 1st January 0001 was a Monday.
2. Calendar repeats after every 400 years.
3. Leap year- it is always divisible by 4, but century years are not leap years unless they are divisible by 400.
4. Odd days- remainder obtained when no. of days is divided by 7. Normal year has 1 odd day and leap year has 2 odd days.
5. Calendar moves ahead by number of odd days.
6. While checking leap year just analyze whether February falls in that period or not.
7. Century has 5 odd days and leap century has 6 odd days.
8. Take out net odd days.( add all the odd days and again divide by 7)
9. In a normal year 1st January and 2nd July and 1st October fall on the same day. In a leap year 1st January 1st July and 30th September fall on the same day.
10. 1st January 1901 was Tuesday.
11. We calculate odd days on the basis of the previous month.

Example – what day is it on 29th August 1982?
Method- As we know 1/1/1901 was a Tuesday now we take 1982 and 1901
– 1982-1901=81 years.
– 81/4=20…. ( disregard decimal)
– 81+20=101
– 101/7- remainder is 3, so 3 days from Tuesday is Friday.
-Now check whether it is a leap year or not. In this case it is not a leap year. Therefore 2nd July will be Friday
– Now we have to go month wise . 2nd august = 3odd days= so from Friday 3 odd days will be Monday so 29th August will be a Sunday.

  1. A product is made by mixing two kinds of metals in the ratio of 1:3 and the costs are in the ratio of 5:2. If it is sold at 50% profit to the retailer, who adds 25p and sells it at Rs. 8.50 per Kg. What is the C.P. of each per Kg.
    2. Raghu wanted to sell something at a profit of 15%, then his C.P. decreased by 5.Raghu decided to earn a profit of 20%, but in totality he received Rs. 3000 less than before. What was the C.P. of the article.
    3. If a shopkeeper marks his goods 50% above the C.P., but he gives 2 articles free if a person purchases 20 articles. Further the shopkeeper gives a discount of 10%. I a customer bought 230 Articles. What is the profit%.
    4. I bought 40 lts. Of milk for Rs. 600, when I went to sell it, I made a loss of as much money, which I received by selling 10 lts, what is my S.P.
    5. A company invested Rs. 200 crores. Manufacturing cost comes to Rs. 6000 per unit for the 1st 10000 units, after that it reduces to 5000 per unit. If it is being sold at Rs. 8000 per unit, what is the break even point in terms of unit and in terms of sale.
    6. A company manufactures computer chips in lots of Rs 100, if any defective chips found, the co. has to pay Rs. 50 per chip, so it can give its chip s for checking , 1st co. charges Rs. 2000 for checking 100 chips, but it can correct only 80% of the chips, another company charges Rs3000, but it corrects all the chips.
    a. upto how many wrong chips per 100 we shud not use any rectification process.
    b. At what level we should prefer 2nd rectification process over the 1st.

    7. A contractor hired 30 men to complete a job in 50 days with 8 hrs, of working, 30 days passed and only 25% work was complete. He called some extra worker and made them work for 12 hrs in a day and he completed the work in time, How many more men did he employ.
    8. A can finish a work in 9 days , B in 15 days, after how many days B should join so that work is completed on the 6th day.
    9. 5 women & 7 men can complete a work in 8 days, 3 women & 10 men complete it in 6 days, then 10 men and 10 women will complete the work in how many days.
    10. In a garrison there is food for 10000 men and it lasts for 1 month if 2kg per head is given everyday. Due to a war 10000 more men join and ration was reduced to 1.5 kgs. And the food got over by 10th day. If instead of 10000 men 5000 men would have joined and the earlier supply would have continued. Than food would have lasted for how many days.

1. John dropped a ball from a height of 8 feet. Everytime it bounces from half the distance it has come. What is the distance traveled by the ball before it comes to rest.
2. Product of 5 consecutive terms is 2000. what is the 1st and last term, and what is the ratio.
3. What is the smallest number that is divided by 8,9 leaving a remainder of 3 in both the cases.
4. What is the smallest number that is divided by 5 and 8 leaving a remainder of 2 and 5 respectively.
5. Number of factors of 72? Out of these how many are odd? How many will be perfect squares? How many will be prime factors.
6. What does (999)* 999*999………… 99 times end with?
7. What is the remainder if 14*14*14……… 23 times is divided by 15?
8. What is the remainder when 7*7*7…… 84 times is divided by 342.
9. Numbers of zero’s at the end of product of 100 prime numbers.
10. A is 25% more than B. B is how much % less than A.
11. A train met with an accident and traveled with 5/6th of the original speed from them. It was late by 15 minutes had the accident occurred 150 mts. Further. It would have been late by only 7 minutes. What is its usual speed.
12. The temperature from Monday to Friday were in proportion , on Monday it was 30 and Friday 53.33. what is the temperature on Thursday.
13. 15 men, 10 women and 20 children went to lucknow for a picnic. Total money spent was Rs. 30000 and it was spent in the ratio of 4:3:4, between men, women and children. How much does each spend and in what ratio?
14. In an alloy, 2 metals are mixed in the ratio of 2:3 and their cost are in the ratio of 5:2, If that alloy is sold @ of 200/kg at 25% profit. What is the cost of each metal separately.
15. A beats B by 30 mts in a 100 mts. Race , B beats C by 40 mts. In a 100 mts. Race, A will defeat C by how much in a 400 mts race.

PARTNERSHIP

1. Capital = money put in the beginning =investment * months
2. Net Capital or net investment =capital* time
3. Time should always be calculated in months or days.
4. Profits are distributed in the ratio of net capital.
5. If capitals are given in the form of fraction like A=1/3, B = 3/5, C=4/7
Then capitals are in the ratio of 35:63:60 ( using LCM method)
6. Sleeping Partner- who gets share of profit only, after everything is subtracted from the profit.
7. Working partner- he gets some money for working. This money is to be subtracted from the total profit and then he gets his due share from the new profit.
8. If a partner takes loan at a certain interest then interest is added to the profit, but in the end he also gets back his share of interest in share of profit.

9. Taxes are reduced from the original profit before hand. But individual income tax is given after distribution of profits.

.Simplify. (26.21*26.21-14.79*44.79)/4.1*26.21-4.1*14.79
2. The HCF of 2 nos. is 113 and their LCM is 228825. One of the no. is 2825. Find the other.
3. The LCM of 2 nos. is 28 times of their HCF. The sum of their LCM and HCF is 1740. If one of the nos. is 240, Find the other no.
4. The sum of 2 nos. is 684 and their HCF is 57. Find all the possible pairs of such numbers.
5. Three plots having an area of 132, 204 and 228 square mts. Respectively are to be sub-divided into equalized flower beds. If the breadth of a bed is 3mts., find the maximum length that a bed can have.
6.There are 408 boys and 312 girls in a school which are to be divided into equal sections of either boys or girls alone. Find the maximum number of boys or girls that can be placed in a section. Also find the total number of sections thus formed.
7. A wine seller had three types of wine , 403 gallon of 1st type,434 gallon of 2nd type, 465 gallon of 3rd type. Find the least possible number of casks of equal size in which different types of wine can be filled without mixing.
8. Four bells ring at intervals of 6,8,12 and 18 seconds. They start ringing simultaneously at 120’ clock. Find when they will again ring simultaneously ? how many times will they ring simultaneously in 6 minutes.
9. 3 equal circular wheels revolve round a common horizontal axis with different velocities. The first makes a revolution in 5 1/3 minutes, 2nd in 2 6/7 minutes and the 3rd in 3 3/7 minutes. 3 markings one in each wheel , are in horizontal line at a certain moment. What is the shortest interval after which they will be in horizontal line again.

10. A,B,C start at the same time from the same place in the same direction to walk round a circular course 12 miles long. A,B,C walk respectively at the rate of3,7 and 13 miles per hour. In what time will they come together again at starting point?
11. A gardener planted 103041 trees in such a way that a number of rows were as were the trees in a row, find the number of rows.
12. On 26th January 1986, students of a school were made to stand in several rows. Each row had as many students as were the total no. of rows. If the total number of students was 1024, how many students were standing in each row?
13. Find the least number by which when added to or subtracted from 1850 makes it a perfect square.
14. If the sum of 2 nos. be multiplied by each separately, the products so obtained are 2418 and 3666. Find the nos.
15. If a number of four digits a, b, c, d in the given order is to be divided by 7, then 2b+3c+d-a must be divisible by 7. of the numbers 0119,1067,5327,and6875 which numbers are divisible.
16. The sides of a triangular field are of lengths 2646, 5157 and 5634 mts. Find the greatest length of the tape by which the three sides may be measured completely.
17. Find the least number divisible by each of the number 21,36,66. How many numbers are there less than 10000 which are divisible by 21,36, and 66?
18. Find the number between 2500 and 3000 which are divisible by 21, 24and 28.
19. Find the side of largest possible square slabs which can be paved on the floor of a room 5m 44 cm long and 3m 74 cm broad. Also find the number of such slabs required to pave the floor.
20. A heap of pebbles when made up into groups of 32,40,72 then the remainders are respectively 10,18 and 50. find the least number of pebbles in the heap.

Answers.
1. 10
2. 9153
3. 420
4. 57,627and 285,399
5. 4mts.
6. 24,30
7. 42
8. 1min. 12 sec.,5 times
9. 4hrs.
10. 12hrs.
11. 321
12. 32
13. 86
14. 47,31
15. 0119,5327
16. 9 mts.
17. 2772,5544,8316
18. 2520 2688,2856
19. 34cms,176
20. 1418

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