A shopkeeper marks his goods at 40% above the cost price but allows a discount of 5% for cash payment to his customers.
Question:
A shopkeeper marks his goods at 40% above the cost price but allows a discount of 5% for cash payment to his customers. What actual profit does he make, if he receives Rs 1064 after paying the discount?
Solution:
Let the original cost price of the item be Rs. $x$.
$\mathrm{MP}=x+\frac{40 x}{100}=1.4 x$
Discount $=M P-S P$
$\mathrm{MP}-\frac{\text { Discount } \% \times \mathrm{MP}}{100}=\mathrm{SP}$
$1.4 x-\frac{5 \times 1.4 x}{100}=1064$
$\frac{1.4 x \times 100-5 \times 1.4 x}{100}=1064$
So, $x(1.4)(0.95)=1064$
$x=\frac{1064}{(1.4 \times 0.95)}$
$=\frac{1064}{1.33}$
$=$ Rs. 800
Profit $=$ Rs. $(1064-800)$
$=$ Rs. 264
Thus, the actual profit by the shopkeeper is Rs. 264 .