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In a mixture of sugar and salt, sugar is 35% by weight of the mixture, half of the mixture is taken out and 31 kg of sugar is added and the ratio of sugar and salt in the mixture becomes 4 ∶ 3. What was the weight of the mixture initially?

In a mixture of sugar and salt, sugar is 35% by weight of the mixture, half of the mixture is taken out and 31 kg of sugar is added and the ratio of sugar and salt in the mixture becomes 4 ∶ 3. What was the weight of the mixture initially? Correct Answer 120 kg

Let the initial weight of the mixture be 100x kg

∴ Quantity of sugar in the mixture = 35x 

Quantity of salt in the mixture = 65x

Now, half of the mixture is taken out

∴ Quantity of sugar left after removal = 35x – 35x/2 = 17.5x

Quantity of salt left after removal = 65x – 65x/2 = 32.5x

After adding 31 kg of sugar sugar and salt in the mixture becomes 4 ∶ 3

∴ (17.5x + 31)/32.5x = 4/3

⇒ 52.5x + 93 = 130x

⇒ 77.5x = 93

⇒ x = 1.2

∴ Weight of the mixture initially = 100 × 1.2 = 120 kg 

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