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The cost prices of articles A and B are the same. A is sold at 20% profit, whereas B is sold for Rs. 54.60 more than the selling price of A. If the overall profit earned on selling A and B is 28%, then what is the cost price of each article?
1. Rs. 348
2. Rs. 345
3. Rs. 341.25
4. Rs. 342.75

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Correct Answer - Option 3 : Rs. 341.25

Given:

A is sold at 20% profit, B is sold for Rs. 54.60 more than the selling price of A

The overall profit earned on selling A and B is 28%

Formula used:

Profit = Selling price – Cost price

SP = [(100 + profit %)/100 × CP]

Calculation:

Let C.P of A nd B be Rs. x

According to the question:

S.P of A = (x × 120/100) = 6x/5

S.P of B = (6x/5 + 54.60)

Total C.P = Rs. (x + x) = Rs. 2x

Total S.P = (6x/5 + 54.60 + 6x/5)

⇒ (12x/5 + 54.60)

Profit = (12x/5 + 54.60 – 2x)

⇒ 2x/5 + 54.60

Now,

⇒ 28% of 2x = 2x/5 + 54.60

⇒ [(28/100) × 2x] = 2x/5 + 54.60

⇒ [(28/100) × 2x] = [2x/5 + (5460/100)]

⇒ [(28/100) × 2x] = (4x + 546)/10

⇒ 28x = 20x + 2730

⇒ 8x = 2730

⇒ x = 2730/8 = Rs. 341.25

∴The cost price of each article is Rs. 341.25.

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