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A mixture of sugar, Rice and wheat in the ratio of 2 ∶ 3 ∶ 4 by volume is required. A shopkeeper wishes to measure out quantities by weight. He finds that the weight of one cubic foot of sugar is 52 kg, of rice 88 kg and of wheat 130 kg. What should be the ratio of sugar, rice, and wheat by weight in order to give a proper mixture?
1. 11 ∶ 13 ∶ 56
2. 11 ∶ 31 ∶ 56
3. 13 ∶ 33 ∶ 65
4. 11 ∶ 13 ∶ 65

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Correct Answer - Option 3 : 13 ∶ 33 ∶ 65

Given:

A mixture of sugar, Rice and wheat in the ratio of 2 ∶ 3 ∶ 4 by volume.

One cubic foot of sugar = 52 kg

One cubic foot of rice = 88 kg 

One cubic foot of wheat = 130 kg

Concept used:

Ratio method is used.

Calculation:

Let the volume of sugar, Rice and Wheat be 2x, 3x and 4x cubic foot.

2x cubic foot of sugar = 2x × 52 kg

3x cubic foot of rice = 3x × 88 kg  

4x cubic foot of wheat = 4x × 130 kg

The ratio of sugar, rice, and wheat by weight = (2x × 52) ∶ ( 3x × 88) ∶ ( 4x × 130)

⇒ the required ratio = 13 ∶ 33 ∶ 65

∴ The ratio of sugar, rice, and wheat by weight 13 ∶ 33 ∶ 65.

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