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50 kgs of rice is sold by the shopkeeper. He sold part of some rice at the profit of 8% and rest at the profit of 18%. Overall profits of 14% are made on the sale. What amount of the quantity of rice was sold at 18% profits.


1. 20 kg
2. 30 kg
3. 35 kg
4. 15 kg

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Correct Answer - Option 2 : 30 kg

Given:

50 kgs of rice is sold by the shopkeeper.

He sold part of some rice at the profit of 8% and rest at the profit of 18%. Overall profits of 14% are made on the sale.

Concepts used:

Profit % = (Profits/C.P.) × 100

Profits = S.P. – C.P.

Calculation:

Let quantity of rice sold at 8% profits be x kg.

⇒ Quantity of rice sold at 18% profits = (50 – x)

Let C.P. of 1 kg rice be Rs. y per kg.

Profit % for x kg rice = 8

⇒ {(S.P. – xy)/xy} × 100 = 8

⇒ S.P. = 27xy/25

Profit % for (50 – x) kg rice = 18

⇒ 18 = {(S.P. – (50 – x)y)/(50 – x)y} × 100

⇒ S.P. = 59 × (50 – x )y/50 = 59y – (59xy/50)

⇒ Total S.P. = 27xy/25 + 59y – 59xy/50 = 59y – (5xy/50)

Overall profits = 14%

⇒ 14 = [{59y – (5xy/50) – 50y}/50y] × 100

⇒ x = 20

⇒ Quantity sold at 18% profits = 50 – x = 50 – 20 = 30 kg

Quantity of rice sold at 18% profits is equal to 30 kg.

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