CAT Quantitative Aptitude Questions | CAT Percentages Problems - Variables

The question is from CAT Percentages. CAT exam is known to test on basics rather than high funda ideas and 2IIMs CAT question bank provides you with CAT questions that can help you gear for CAT Exam CAT 2023. This is a very interesting question on the topic percentages using Variables.When thieves share loot, things always get interesting!!!

Question 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% , A got Rs.40 more than D
2. 80% , A got Rs.20 more than D
3. 175% , A got Rs.50 more than D
4. 150% , A got Rs.35 more than D

Explanatory Answer

Method of solving this CAT Question from Percentages: Comparison of loot among thieves.

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) ------(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 = \\frac{c}{c}\\) + 1 ------(2)
b = 2a -------(3)
Substituting, Equations (2) in and (3) in (1), we get
\\frac{c}{2(c + 1)}\\) = \\frac{1 - c}{c + 1}\\), or c = 2 - 2c, or c = \\frac{2}{3}\\)
b = \\frac{c}{c + 1}\\) = \\frac{2}{5}\\) , a = \\frac{1}{5}\\)
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).

The question is " 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.

Hence, the answer is 160% , A got Rs.40 more than D

Choice A is the correct answer.