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Question 481133: a man purchases a certain number of mangoes at the rate of 3 per rupee and the same number at the rate 4 per rupee. He mixes them together and sells them at the rate of 3 per rupee. what is his gain or loss percent?
(A) 7% (B) 8% (C) 13% (D) 100/7 (E) 49/3
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! he buys a certain number at 3 mangoes per rupee.
he buys the same number at 4 mangoes per rupee.
he mixes them together and sells them at 3 mangoes per rupee.
let x = number of mangoes he buys.
if he gets 3 mangoes for 1 rupee, then his cost per mango is r/3.
if he gets 4 mangoes for 1 rupee, then his cost per mango is r/4.
he buys x at r/3 each for a total cost of xr/3.
he buys x at r/4 each for a total cost of xr/4.
his total cost is xr/3 + xr/4 which becomes 7xr/12.
when he sells the mangoes, he sells them for 3 mangoes per rupee.
his revenue for each mango is therefore equal to r/3.
his total revenue is equal to 2x * r/3 which is equal to 2xr/3.
he has a total revenue of 2xr/3.
he has a total cost of 7xr/12.
his total profit is equal to his total revenue minus his total cost.
this becomes 2xr/3 - 7xr/12 which becomes xr/12.
his rate of profit is equal to his total profit divided by his total cost.
this becomes xr/12 divided by 7xr/12.
this is equivalent to xr/12 times 12/7xr which results in a rate of profite of 1/7.
if his rate of profit is 1/7, then his percent profit is equal to 100% times that.
his percent profite would therefore be 100/7% which is equal to 14.28571429%.
that is not one of your selections, but 100/7 is, so your answer is 100/7 which is selection D.
you can confirm this by plugging in some numbers.
suppose he buys 12 mangoes at 3 mangoes per rupee.
he pays 12/3 = 4 rupees.
suppose he then buys 12 mangoes at 4 mangoes per rupee.
he pays 12/4 = 3 rupees.
his total cost is 7 rupees.
he now sell all 24 mangoes at 3 mangoes per rupee.
he collects 24/3 = 8 rupees.
his revenue is 8 rupees.
his cost is 7 rupees.
his profit is 1 rupee.
his rate of profit is 1/7
his percent profit is 100/7
number check out so the formulas are good.
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