Question

A trader purchases a watch and a wall clock for Rs. 390. He sells them making a profit of 10% on the watch and 15% on the wall clock. He earns a profit of Rs. 51.50. The difference between the original prices of the wall clock and the watch is equal to

• A. Rs. $110$
• B. Rs. $90$
• C. Rs. $100$
• D. Rs. $80$

Answer 1

Answer: (A)

Let original price ( Cost price ) of watch be $xRs$

Then Original price of wall clock $=390-xRs$

Trader earns profit of 10% on watch.

$\therefore SPofwatch=CPofwatch+Profit$

$\Rightarrow S{P}_1=x+10\%ofx=\frac{11x}{10}$

Also, trader earns profit of % on wall clock.

$\therefore SPofwallclock=CPofwallclock+Profit$

$\Rightarrow S{P}_2=(390-x)+15\%of(390-x)$

$\Rightarrow S{P}_2=(390-x)+(58.5-\frac{3x}{20})$

$\therefore TotalSellingPrice\left(SP\right)=S{P}_1+S{P}_2$

$=\frac{11x}{10}+390-x+58.5-\frac{3x}{20}$

$=448.5-\frac{x}{20}$

It is given that trader earns a profit of 51.50 Rs

$\Rightarrow SP-CP=51.50$

$\Rightarrow (448.5-\frac{x}{20})-390=51.50$

$\Rightarrow 58.5-\frac{x}{20}=51.50$

$\Rightarrow \frac{x}{20}=7$

$\therefore x=20\times 7=140$

It means original price of watch $=x=140Rs$ and original price of wall clock $=390-x=390-140=250Rs$

So, Difference in price $=250-140=110Rs$