Question

A merchant marks his goods at $25\%$ above the cost price. Due to slump in the market, his cost reduces by $5\%.$ He thus offers a discount of $8\%,$ due to which the sales go up by $25\%.$ Compute the change in the merchant's profit.

• A. $5\%$ higher
• B. $7\frac{1}{2}\%$ higher
• C. $8\%$ lower
• D. unchanged

Answer 1

The correct option is D unchanged

Let the C.P. of each article be $100$ rupees and the number of articles sold be $x.$
Then, original S.P. $=125$ rupees
Original profit $=(125-100)x=25x$

Now, new C.P. $=95$ rupees
New S.P. $=92\%$ of $125$
$=(\frac{92}{100}\times 125)=115$ rupees
Number of articles sold now $=1.25x$
New profit $=\left(1.25x\right(115-95\left)\right)=25x$
Hence, the profit remains unchanged.