Question

Ramesh bought two boxes for Rs. 1300. He sold one box at a profit of $20\%$ and the other box at a loss of $12\%$. If the selling price of both boxes is the same, find the cost price of each box.

Answer 1

Total cost price of two boxes = Rs. 1300
S.P of each box is same.
Let S.P of each box = Rs. 100
S.P of first box = Rs. 100
Gain $=20\%$
C.P $=\frac{S.P\times 100}{100+gain\%}=\frac{100\times 100}{100+20}=Rs.\frac{10000}{120}$
S.P of second box = Rs. 100
Loss $=12\%$
$\therefore$ C.P $=\frac{S.P\times 100}{100-Loss\%}=\frac{100\times 100}{100-12}=\frac{10000}{88}$
Now ratio in their C.P's
$=\frac{10000}{120}:\frac{10000}{88}=\frac{1}{120}:\frac{1}{88}=88:120=11:15$
Sum of ratio's = 11 + 15 = 26
$\therefore$ C.P of first box $=Rs.\frac{1300\times 11}{26}$
= Rs. 550
and C.P of second box $=Rs.\frac{1300\times 15}{26}$
= Rs. 750