# A shopkeeper bought two bicycles at Rs. 8,000. He sold one bicycle at 20% profit and another bicycle at 30% loss. On the whole there is neither profit

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A shopkeeper bought two bicycles at Rs. 8,000. He sold one bicycle at 20% profit and another bicycle at 30% loss. On the whole there is neither profit nor loss. Find the cost price of the second bicycle.
1. Rs. 3,000
2. Rs. 3,500
3. Rs. 3,200
4. None

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Correct Answer - Option 3 : Rs. 3,200

Given:

Total C.P of bicycle = 8000

Percent profit on 1st bicycle = 20%

Percent loss on 2nd bicycle = 30%

Total C.P = total S.P

Formula Used:

Percent profit/loss = (profit/loss)/C.P × 100

Concept used:

Profit and loss is always calculated on C.P

Calculation:

Total C.P = 8000

Let, C.P of 1st bicycle = X and C.P of 2nd bicycle = Y

X + Y = 8000     ---- (1)

There is no profit no loss, total C.P = total S.P = 8000

Profit on 1st bicycle = loss on 2nd bicycle

⇒ 20% of X = 30% of Y

⇒ X/Y = 3/2 or X ∶ Y = 3 ∶ 2

⇒ Y = (2/5) × 8000 = 3200

∴ The C.P of 2nd bicycle is Rs. 3200.