CAT Practice : Percents, Profits

When thieves share loot, things always get interesting.

Percentages - Variables

    Q.6: A, B, C and D share a loot. A gets a% of the total. B gets b% of the remaining (after A has taken his share). C gets c% of the remaining and D gets the rest. D gets a% less than what A gets, B and C get equal amounts. b = 2a.
    1.   What percentage of what A got did C get?
    2.   If the total amount is equal to Rs. 1000, what is the difference between what A got and what D got?

    1. 160%
    2. 80%
    3. 175%
    4. 150%

 

  • Correct Answer
    Choice A. 160%

Detailed Solution

Let total amount = T.

A would have got T * a. After A takes his share, there would be T (1 - a) left
B would have got T (1 - a) * b
C would have got T (1 - a)(1 - b) * c
D would have got T (1 - a) (1 - b) (1 - c)

D gets a % less than what A gets, or, T *a (1 - a) = T(1 - a) (1 - b) (1 - c), or
a = (1 - b)(1 - c)   -------- Eqn 1

B and C get the same amounts, or (1 - a) * b = (1 - a) * (1 - b) * c, or b = (1 - b) c, or, b = c - cb, or
b = + 1   ------------ Eqn 2
b = 2a   -----------------Eqn 3

Substituting, eqn 2 in and 3 in eqn 1, we get

Or, c = 2 -2c, or c =

b = , a =

a gets 20% of the loot, b gets 40% of the remaining 80%, or 32% of the loot. C gets 66.6% of 48%, or 32% of the overall loot. And d gets the final 16% of the overall amount (20% lesser than A's share).

Now, to the questions,

  1. What percentage of what A got did C get?
    A got 20% of overall, C got 32% of overall. Or, C got 160% of A

  2. If the total amount is equal to Rs. 1000, what is the difference between what A got and what D got?
    A would have got Rs. 200, D Rs. 160. A would have got Rs. 40 more than D.

Correct Answer: 160%



Our Online Course, Now on Google Playstore!

2IIM's App

Fully Functional Course on Mobile

All features of the online course, including the classes, discussion board, quizes and more, on a mobile platform.


Cache Content for Offline Viewing

Download videos onto your mobile so you can learn on the fly, even when the network gets choppy!

Get it on Google Play
Visit Piverb.com
Visit Wizako.com