Question

The profit percentage of the three articles A, B, and C is 10%, 20%, and 25% and the ratio of the cost price is 1 : 2: 4. Also, the ratio of the number of articles sold of A, B and C is 2: 5: 2. Then, the overall profit percentage is :

• A. 18.5%
• B. 21%
• C. 75%
• D. None of these

Answer 1

The correct option is B 21%

Let CP of A, B, C be 100, 200, and 400 respectively.
Then profit for A, B, C = 10, 40, and 100 respectively.
Let the number of articles sold be 2, 5, 2 respectively for A, B, and C.
Total profit = $2\times 10+5\times 40+2\times 100=420$
Total CP = $2\times 100+5\times 200+2\times 400=2000$
Overall profit percentage = $\frac{420}{2000}\times 100=21\%.$

Alternate Approach:
CP of $A+B+C=2x\times y+5x\times 2y+2x\times 4y=20xy$
Profit of A = 0.2xy
Profit of B = 2xy
Profit of C = 2xy
Total profit = 4.2xy
$\%profit=\frac{4.2xy}{20xy}\times 100=21\%$