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?
Answers
Solution :-
Let us assume that, total amount of loot is Rs. x .
so,
→ A gets = a% of x = Rs. xa
then,
→ Remaining amount = (x - xa) = Rs. x(1 - a)
now,
→ B gets = b% of x(1 - a) = Rs. bx(1 - a)
then,
→ Remaining amount = x(1 - a) - bx(1 - a) = Rs. x(1 - a)(1 - b)
now,
→ C gets = c% of remaining = Rs. xc(1 - a)(1 - b)
then,
→ Remaining amount = {x(1 - a)(1 - b)} - {xc(1 - a)(1 - b)} = Rs. x(1 - a)(1 - b)(1 - c) = D gets .
now, given that,
- D gets a% less than what A gets .
- B and C get equal amounts => b = 2a .
so,
→ D gets = a% less than A
→ x(1 - a)(1 - b)(1 - c) = xa - (a% of xa)
→ x(1 - a)(1 - b)(1 - c) = xa - xa²
→ x(1 - a)(1 - b)(1 - c) = xa(1 - a)
→ (1 - b)(1 - c) = a ---------- Eqn.(1)
also,
→ B gets = C gets
→ bx(1 - a) = xc(1 - a)(1 - b)
→ b = c(1 - b)
→ b = c - cb
→ b + cb = c
→ b(1 + c) = c
→ b = (c/1 + c) --------- Eqn.(2)
also, given that,
→ b = 2a
→ a = (b/2) ---------- Eqn.(3)
putting Eqn.(3) in Eqn.(2)
→ a = {c/2(1 + c)} --------- Eqn.(4)
now, putting Eqn.(2) and Eqn.(4) in Eqn.(1)
→ [1 - (c/1 + c)] * (1 - c) = c/2(1 + c)
→ [(1 + c - c)/(1 + c)] * (1 - c) = c/2(1 + c)
→ (1 - c)/(1 + c) = c/2(1 + c)
→ 1 - c = c/2
→ 1 = c + c/2
→ 1 = 3c/2
→ c = (2/3)
putting value of c in Eqn.(2) ,
→ b = (2/3)/[1 + 2/3)]
→ b = (2/3)[(5/3)
→ b = (2/3) * (3/5)
→ b = (2/5)
putting value of b in Eqn.(3) ,
→ a = (2/5) / 2
→ a = (2/5) * (1/2)
→ a = (1/5) .
therefore,
→ A gets = (1/5) * 100 = 20% of total .
→ B gets = (2/5) of (100% - 20%) = 32% of total .
→ C gets = (2/3) of (80% - 32%) = (2/3) * 48% = 32% of total .
→ D gets = 100% - (20% + 32% + 32%) = 16% of total .
now, Solving (1) :-
→ % of that A got did C get = Meaning = C gets what % of A = 32% is what % of 20% = (32 * 100) / 20 = 160% (Ans.)
Solving (2) :-
→ Total amount = Rs.1000
→ A gets = 20% of 1000 = (20 * 1000)/100 = Rs.200
→ D gets = 16% of 1000 = (16 * 1000)/100 = Rs.160
then,
→ Required difference = 200 - 160 = Rs.40 (Ans.)
{ Values are taken in % . }
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