Question

If a shopkeeper sells $\frac{1}{3}$rd of his goods at a profit of $14\%$, $\frac{3}{5}$th of the goods at a profit of $17.5\%$ and remaining at a profit of $20\%$, then his profit on the whole is equal to

• A. $15.5\%$
• B. $16\%$
• C. $16.5\%$
• D. $17\%$

Answer 1

The correct option is C $16.5\%$

Let total cost of all goods be Rs. $100$.
He sold $\frac{1}{3}$ of his goods that is Rs. $33.3$ at a profit of $14\%$
Then profit $=33.3\times \frac{14}{100}=$ Rs. $4.662$
Simillarly $\frac{3}{5}=60$, Profit $17.5\%$
Then profit $=60\times \frac{17.5}{100}=0.60\times 17.5=10.5$
Now $100-(33.3+60)=100-93.3=$ Rs. $6.7$
Profit on Rs. $6.7=\frac{6.7\times 20}{100}=1.34$
Total profit $=4.662+10.5+1.34=$ Rs. $16.502=16.5\%$