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.