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How many kg of wheat costing R8 must be mixed with 36 kg of rice costing Rs. 5.40 per kg so that 20% gain may be obtained by selling the mixture at Rs. 7.20 per kg?Options :10kg12kg9.8kg10.8kg

Question

How many kg of wheat costing R8 must be mixed with 36 kg of rice costing Rs. 5.40 per kg so that 20% gain may be obtained by selling the mixture at Rs. 7.20 per kg?Options :10kg12kg9.8kg10.8kg

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Solution

Let's denote:

  • The cost price of wheat as W (in this case, W = R8 per kg)
  • The cost price of rice as R (in this case, R = Rs. 5.40 per kg)
  • The selling price of the mixture as S (in this case, S = Rs. 7.20 per kg)
  • The weight of wheat to be mixed as x kg
  • The weight of rice already present as y kg (in this case, y = 36 kg)

We know that a 20% gain is obtained by selling the mixture. This means that the cost price of the mixture is 80% of the selling price. Therefore, we can write the equation:

0.8 * S = (Wx + Ry) / (x + y)

Substituting the given values:

0.8 * 7.2 = ((8x + 5.436) / (x + 36))

Solving this equation for x, we get x = 10.8 kg.

So, 10.8 kg of wheat must be mixed with the 36 kg of rice. The correct option is 10.8 kg.

This problem has been solved

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