Question

A man sold a chair and a table together for $Rs.1520$ thereby making a profit of $25$% on chair and $10$% on table. By selling them together for $Rs.1535$ be would have made a profit of $10$% on the chair and $25$% on the table. Find cost price of each.

• A. Cost price of chair $=Rs.800$
  and Cost price of table $=Rs.500$
• B. Cost price of chair $=Rs.600$
  and Cost price of table $=Rs.700$
• C. Cost price of chair $=Rs.300$
  and Cost price of table $=Rs.1200$
• D. Cost price of chair $=Rs.900$
  and Cost price of table $=Rs.800$

Answer 1

The correct option is B Cost price of chair $=Rs.600$

and Cost price of table $=Rs.700$

Let the cost price of chair $=Rs.x$
and cost price of table $=Rs.y$
ATP
$\frac{125x}{100}+\frac{110y}{100}=1520$
$125x+11oy=\mathrm{152000........}\left(i\right)$
and $\frac{110x}{100}+\frac{125y}{100}=1535$
$110x+125y=\mathrm{153500.......}\left(ii\right)$
Add $\left(i\right)$ and $\left(ii\right)$
$235x+235y=305500$
$x+y=\mathrm{1300.......}\left(iii\right)$
Substract equation $\left(ii\right)$ from $\left(i\right)$
$15x-15y=-1500$
$x-y=-\mathrm{100......}\left(iv\right)$
Now,
$x+y=1300$
$x-y=-100$
--------------------
$2x=1200$
$x=600$
Put $x=600$ in equation $\left(iii\right)$
$600+y=1300$
$y=700$
So, cost price of chair $=Rs.600$
and cost price of table $=Rs.700$