Question

$A$ sold a table to $B$ at a profit of $15\%$, later on, $B$ sold it back to $A$ at a profit of $20\%$ thereby gaining Rs. $69$. How much did $A$ pay for the table originally?

• A. Rs. $300$
• B. Rs. $400$
• C. Rs. $500$
• D. Rs. $600$

Answer 1

The correct option is A Rs. $300$

Given, when $B$ sells the table to $A$,
Profit $\%$ $=20$
Gain $=$ Rs. $69$
Profit $\%$ $=\frac{Gain}{C.P.}\times 100=20$
$\Rightarrow \frac{69}{C.P.}\times 100=20$
$\Rightarrow$ C.P. $=$ Rs. $345$
This CP of $B$ is the SP for $A$, as $A$ sold the table to $B$ first.
Given, when $A$ sells the table to $B$,
Profit $\%$ $=15$
So, at SP $=$ Rs. $345$, we have
Profit $\%$ $=\frac{S.P.-C.P.}{C.P.}\times 100=15$
$\Rightarrow \frac{345-C.P.}{C.P.}\times 100=15$
$\Rightarrow 345-C.P.=0.15C.P.$
$\Rightarrow 1.15C.P.=345$
$\Rightarrow$ C.P. $=$ Rs. $300$
Thus, $A$ bought the table first for Rs. $300$.