Q6. **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. **

** What percentage of what A got did C get? **** If the total amount is equal to Rs. 1000, what is the difference between what A got and what D got?**

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) ------(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 = c/c + 1

b = 2a -------(3)

Substituting, Equations (2) in and (3) in (1), we get

c/2 (c+1) = 1−c/c+1, or c = 2 - 2c, or c = 23; b = c/c+1 = 2/5 , a = 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).

A got 20% of overall, C got 32% of overall. Or, C got 160% of A A would have got Rs. 200, D Rs. 160. A would have got Rs. 40 more than D