Question

I bought two tables for Rs. $5400$. I sold one at a loss of $5\%$ and the other at a gain of $7\%$. In the whole transaction, I neither gained nor lost. Find the costs of the tables separately.

• A. Cost of the two tables are Rs. $3790$ and Rs. $2720$.
• B. Cost of the two tables are Rs. $3150$ and Rs. $2250$.
• C. Cost of the two tables are Rs. $2670$ and Rs. $1850$.
• D. None of these
  

Answer 1

Answer: (B)

Cost of the two tables are Rs. $3150$ and Rs. $2250$.

Let the C.P. of one table $=$ Rs. $x$

Then, C.P. of the other table $=$ Rs. $(5400-x)$
S.P. of the first table at a loss of $5\%$ $=$ Rs. $\frac{95}{100}\times x$

S.P. of the other table at a gain of $7\%$ $=$ Rs. $\frac{107}{100}\times (5400-x)$
Since there is no gain no loss.
Total S.P. $=$ Total C.P.

$\Rightarrow \frac{95x}{100}+\frac{107\times (5400-x)}{100}=5400$

$\Rightarrow \frac{95x}{100}-\frac{107x}{100}+\frac{107\times 5400}{100}=5400$

$\Rightarrow \frac{-12x}{100}=\frac{5400\times 100-5400\times 107}{100}$

$\Rightarrow \frac{-12x}{100}=\frac{540000-577800}{100}$

$\Rightarrow -12x=-37800$

$\Rightarrow x=\frac{37800}{12}=$ Rs. $3150$

$\therefore$ Cost of the two tables are Rs. $3150$ and $(5400-3150)=$ Rs. $2250$.