CAT Problems on Profit and Loss Set-3 PDF

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CAT Problems on Profit and Loss:

Question 1:

Five horses, Red, White, Grey, Black and Spotted participated in a race. As per the rules of the race, the persons betting on the winning horse get four times the bet amount and those betting on the horse that came in second get thrice the bet amount. Moreover, the bet amount is returned to those betting on the horse that came in third, and the rest lose the bet amount. Raju bets Rs. 3000, Rs. 2000 and Rs. 1000 on Red, White and Black horses respectively and ends up with no profit and no loss.
Which of the following cannot be true?

a) At least two horses finished before Spotted
b) Red finished last
c) There were three horses between Black and Spotted
d) There were three horses between White and Red
e) Grey came in second

Question 2:

Once I had been to the post office to buy five-rupee, two-rupee and one-rupee stamps. I paid the clerk Rs. 20, and since he had no change, he gave me three more one-rupee stamps. If the number of stamps of each type that I had ordered initially was more than one, what was the total number of stamps that I bought?

a) 10
b) 9
c) 12
d) 8

Question 3:

Two men X and Y started working for a certain company at similar jobs on January 1, 1950. X asked for an initial monthly salary of Rs. 300 with an annual increment of Rs. 30. Y asked for an initial monthly salary of Rs. 200 with a rise of Rs. 15 every 6 months. Assume that the arrangements remained unaltered till December 31, 1959. Salary is paid on the last day of the month. What is the total amount paid to them as salary during the period?

a) Rs. 93,300
b) Rs. 93,200
c) Rs. 93,100
d) None of these

Question 4:

Instead of a metre scale, a cloth merchant uses a 120 cm scale while buying, but uses an 80 cm scale while selling the same cloth. If he offers a discount of 20% on cash payment, what is his overall profit percentage?

a) 20%
b) 25%
c) 40%
d) 15%

Question 5:

Five horses, Red, White, Grey, Black and Spotted participated in a race. As per the rules of the race, the persons betting on the winning horse get four times the bet amount and those betting on the horse that came in second get thrice the bet amount. Moreover, the bet amount is returned to those betting on the horse that came in third, and the rest lose the bet amount. Raju bets Rs. 3000, Rs. 2000 and Rs. 1000 on Red, White and Black horses respectively and ends up with no profit and no loss.
Suppose, in addition, it is known that Grey came in fourth. Then which of the following cannot be true?

a) Spotted came in first
b) Red finished last
c) White came in second
d) Black came in second
e) There was one horse between Black and White

Answers and Solutions for CAT Problems on Profit and Loss:

Solutions:

In total Raju bets 6000Rs and ends up with no profit – no loss. So there are 3 possibilities.
1) White comes 2nd, Black comes 4th and Red comes 5th.
2) Black comes 1st, White comes 3rd and Red comes 4th or 5th.
3) Black comes 2nd, Red comes 3rd and White comes 4th or 5th.
So there can never be 3 horses between white and red according to above to possibilities. Hence option D cannot be true.

As shopkeeper gave 3 one-rupee change for 20 rs. change, Buyer must have ordered for a total of 17 rs. stamps.
Now buyer ordered for at least more than 1 stamp for each type
Hence the minimum he bought was:
2 stamp for 5 rupees = 10 rs.
2 stamp for 2 rupees = 4 rs.
2 stamp for 1 rupee = 2 rs.
For the total to be seventeen, the buyer must have purchased 3 one rupee stamps.
And 3 one rupee stamps were also there as changes given by shopkeeper.
So total number of stamps = 2+2+(3+3) = 10

January 1, 1950 to December 31, 1959 is a period of 10 years or 20 half years.
The person X after 1st year gets Rs. 300 in next year he gets Rs. 330 and so on.
So his earning is in AP with 10 300+330+360+…
Similarly earning of Y is in AP with 20 terms 200+215+230+245…. .
So, the total earnings of X equals 12*(300+330+….10 terms) = 52200
The total earnings of Y equals 6*(200+215+230+…20 terms) = 41100
So, the total earnings of the two equals 52200+41100 = 93300

Lets say the cost of the cloth is x rs per metre. Because of the faulty meter, he is paying x for 120 cms when buying.
So cost of 100 cms = 100x/120. He is selling 80 cms for x, so selling price is 100x/80. discount = 20%
so selling price is .8*100x/80= x
Profit = x – 100x/120 = x/6
Profit % = x/6 divided by 100x/120 = 20%