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Q.

A man sells two articles for the same price Rs, 640. He earns 20% profit on the first and 10% profit on the second. Find the overall percent profit.

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a

14.78 %

b

14.08 %

c

14.28 %

d

14.58 %

answer is A.

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Detailed Solution

Concept- This question will make use of the percentages, profit, and loss concepts. By simply dividing by 100 we can convert percentages into fraction. Relationship between cost price and selling price.

SP = CP + P % Of CP

SP = CP + \frac{P}{100} \times CP

SP = (1 + \frac{P}{100}) \times CP

Let two articles be A and B. Both the articles selling price are the same =Rs.640. Now we will find the total cost price and selling price for both articles and find the overall profit.
For articles A,

{SP}_{A} = (1 + \frac{P_{A}}{100}) C P_{A}

640 = \frac{120}{100} C P_{A}

C P_{A} = Rs . 533.33

For article B,

S P_{B} = Rs . 640

S P_{B} = (1 + \frac{P_{B}}{100}) C P_{B}

840 = (1 + \frac{10}{100}) C P_{B}

640 = \frac{110}{100} C P_{B}

C P_{B} = Rs . 581.82

Now, C P_{TOTAL} = C P_{A} + C P_{B} = 533.33 + 581.22 = Rs . 1115.15

S P_{TOTAL} = S P_{A} + S P_{B} = 640 + 640 = Rs . 1280

Finding net worth,

S P_{TOTAL} = (1 + \frac{P_{NET}}{100}) C P_{TOTAL}

1280 = (1 + \frac{P_{NET}}{100}) 1115.15

\frac{P_{NET}}{100} = \frac{1280}{1115.15} - 1 = 1.1478 - 1 = 0.1478

P_{NET} = 14.78 %

Hence, the correct option is 1.

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