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Wheat costing Rs. 30/kg, Rs. 35/kg and a third variety of wheat are mixed in the ratio of 3 ∶ 4 ∶ 2. If the mixture costs Rs. 34/kg, then what will be the cost (in Rs./kg) of the third variety of wheat?

Wheat costing Rs. 30/kg, Rs. 35/kg and a third variety of wheat are mixed in the ratio of 3 ∶ 4 ∶ 2. If the mixture costs Rs. 34/kg, then what will be the cost (in Rs./kg) of the third variety of wheat? Correct Answer 38

Given:

Wheat costing Rs. 30/kg, Rs. 35/kg and a third variety of wheat are mixed in the ratio of 3 ∶ 4 ∶ 2.

The mixture costs Rs. 34/kg.

Concept :

If N is divided into two part in the ratio a : b, then

First part = N × a/(a + b)

Second part = N × b/(a + b)

Calculation:

Let the quantity of three varieties of wheat be 3x, 4x and 2x and cost of third variety of wheat be Rs. a/kg

According to the question,

⇒ (3x × 30) + (4x × 35) + (2x × a) = 34 × (3x + 4x + 2x)

⇒ 90x + 140x + 2xa = 306x

⇒ 2xa = 76x

⇒ a = 38

∴ The cost of the third variety of wheat is Rs. 38/kg

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