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The prices of houses A and B were in the ratio of 2 : 3 and prices of houses B and C were in the ratio 3 : 5 before repairs. A builder spends 10%, 20% and 30% of the original price of the house on repairs for the houses and sells it without any profit. Find the ratio of the prices at which the houses were sold after the repairs were done.

The prices of houses A and B were in the ratio of 2 : 3 and prices of houses B and C were in the ratio 3 : 5 before repairs. A builder spends 10%, 20% and 30% of the original price of the house on repairs for the houses and sells it without any profit. Find the ratio of the prices at which the houses were sold after the repairs were done. Correct Answer 22 : 36 : 65

The ratio of A to B is 2 : 3 and the ratio of B to C is 3 : 5

Hence the ratio of A to B to C is 2 : 3 : 5

Let the price of house A before repairs be 2x

Builder spends 10% on repairs

0.1 × 2x = 0.2x

The selling price of house A = 2x + 0.2x = 2.2x

The price of house B before repairs is 3x

The builder spends 20% on repairs

0.2 × 3x = 0.6x

The final selling price of house B = 3x + 0.6x = 3.6x

The price of house C before repairs was 5x

The builder spends 30% on repairs

0.3 × 5x = 1.5x

Final selling price of house C = 5x + 1.5x = 6.5x

Ratio of final selling prices of A to B to C is 2.2x : 3.6x : 6.5x

∴ A : B : C = 22 : 36 : 65

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