Question

There are two varieties of wheats. The varieties costs Rs. 70 per kg and Rs. 85 per kg respectively. At what price the mixture of the two varieties must be sold to earn a profit of 10% when they were mixed in the ratio 2 ∶ 3?
1. Rs. 76 per kg
2. Rs. 79 per kg
3. Rs. 83.6 per kg
4. Rs. 86.9 per kg

Answer 1

Correct Answer - Option 4 : Rs. 86.9 per kg

Given:

Cost of first variety = Rs. 70 per kg

Cost of second variety = Rs. 85 per kg

Ratio of the two varieties = 2 ∶ 3

Profit earned = 10%

Formula used:

(Quantity of cheaper/Quantity of dearer) = [(Cost price of dearer) – (Mean price)]/[(Mean price) – (Cost price of cheaper)]

Calculations:

Let the mean price of the mixture be Rs. x per kg

⇒ 2/3 = (85 – x)/(x – 70)

⇒ 2x – 140 = 255 – 3x

⇒ 5x = 395

⇒ x = Rs. 79 per kg

Price of mixture at 10% profit = 79 × (110/100)

⇒ Rs. 86.9 per kg

∴ The mixture must be sold Rs. 86.9 per kg to earn a profit of 10%