Problema Solution
A fruit seller has 24kg apples. He sells at part of this at a gain of 20% and the remaining at the loss of 5%. If he earns a profit of 10% on selling the whole amount of apples. Find the amount of apples sold at a loss.
Answer provided by our tutors
let
C.P = the cost price per kg apples
x = the amount of apples sold at 20% gain that is SP > CP (selling price > cost price)
y = the amount of apples sold at 5% loss that is CP > SP (cost price > selling price)
a fruit seller has 24kg apples
x + y = 25
from the total sell he earns 10% profit
the gain from x kg apples + loss of y kg apples = profit 10% of cost price of 25 kg
x(SP - CP) + y(SP - CP) = 0.10*CP*25
Gain = SP - CP
Loss = - (SP - CP)
Gain % = (Gain x 100)/C.P.
Loss % = (Loss x 100)/C.P.
x(Gain % *CP)/100 - y(Loss% *CP)/100 = 0.10*CP*25 divide both sides by CP and we get
0.20x - 0.05y = 0.10*25
by solving the system of equations
x + y = 25
0.20x - 0.05y = 0.10*25
we find
x = 15 kg
y = 10 kg
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10 kg of apples were sold at lost.