Question

A man buys $100kg$ of sugar for $Rs.2400$. He sold $1/4^{th}$ of the stock at a loss of $5\%$. At what percent profit should he sell the remaining stock so as to make an overall profit of $20\%$ on the whole transaction?

• A. $25\%$
• B. $27\frac{1}{3}\%$
• C. $28\%$
• D. $28\frac{1}{3}\%$

Answer 1

The correct option is D $28\frac{1}{3}\%$

Quantity of sugar $=100kg$

Cost of 100 kg sugar $=Rs.2400$

Sold ${\left(\frac{1}{4}\right)}^{th}$ quantity of sugar at a loss of $5\%$

$\frac{1}{4}$ of $2400=Rs.600$

Cost of 25 kg sugar $=Rs.600$

$Loss=C.P.-S.P.$

$Loss=5\%of600=\frac{(600\times 5)}{100}=Rs.30$

S.P. of 25 kg sugar $=600-30=Rs.570$

Profit required on whole transaction = 20 $\%$ + loss to be recovered of Rs. 30

$20$ of $2400=Rs.480+Rs.30$

Total profit required $=Rs.510$

C.P. of remaining quantity of sugar $=2400-600=Rs.1800$

$\text{Profit percent on whole transaction}=\frac{(510\times 100)}{1800}=\frac{51000}{1800}=28.33\%\approx 28\frac{1}{3}\%$