Question

A man bought two TV sets for $Rs.42500.$ He sold one at a loss of $10\%$

and other at a profit of $10\%$. If the selling price of each TV set is same, determine the cost price of each set.

Answer 1

Let the C.P of first set be $Rs.x$

And, the C.P of the second set will be $Rs.(42500-x)$

S.P of the first set $=\frac{100-\text{loss}\%}{100}\times C.P$

$=\frac{100-10}{100}\times x$ [Given: Loss$\%=10\%$]

$=\frac{9x}{10}$

S.P of the Second set $=\frac{100+\text{Profit}\%}{100}\times C.P$

$=\frac{100+10}{100}\times (42500-x)$ [Given: Profit $\%=10\%$]

$=\frac{11(42500-x)}{10}$

It is given that the selling price of both the T.V set is equal.

$\therefore \frac{9x}{10}=\frac{11(42500-x)}{10}$

$\Rightarrow 9x=11(42500-x)$

$\Rightarrow 9x=42500\times 11-11x$

$\Rightarrow 20x=42500\times 11$

$x=\frac{42500\times 11}{20}$

$\therefore x=2125\times 11=23375$

Hence, the cost price of first T.V set is $Rs.23375$ and for the second one price will be $(42500-23375=Rs.19125)$