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Raman mixed 8 kg of one variety of wheat with x kg of another. If the cost per kg of the two varieties are in the ratio 3 ∶ 2, the ratio of the selling price of the blended wheat per kg to that of the cost price of the superior variety of wheat per kg is 1 ∶ 1 and Raman makes an overall profit of 25% what is the value of x?

Raman mixed 8 kg of one variety of wheat with x kg of another. If the cost per kg of the two varieties are in the ratio 3 ∶ 2, the ratio of the selling price of the blended wheat per kg to that of the cost price of the superior variety of wheat per kg is 1 ∶ 1 and Raman makes an overall profit of 25% what is the value of x? Correct Answer 12

Calculation:

Let the cost per kg of the two varieties of wheat be 3y kg and 2y kg.

Then, the Cost Price of the two types of wheat be

⇒ 3y × 8 + 2y × x

⇒ 24y + 2 xy

⇒ Rs 24y + 2 xy

Then,

The Selling Price of the mixture = {(100 + 25)/100} × (24y + 2 xy)

The Selling Price of the mixture = 1.25 × (24y + 2xy)

The Selling Price of the mixture = Rs. 30y + 2.5 xy

The selling price of the blended wheat per kg = (30y + 2.5 xy)/(8 + x)

The cost price superior variety of wheat per kg is 3y.

Now, A/Q

{(30y + 2.5 xy)/(8 + x)} ∶ 3y = 1 ∶ 1

⇒ (30 + 2.5 x)/(8 + x) = 3

⇒ 30 + 2.5x = 3(8 + x)

⇒ 30 + 2.5x = 24 + 3x

⇒ 0.5x = 6

⇒ x = 12

∴ The value of x is Rs 12

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