In a bucket, paint and oil are in the ratio 7 : 5. 24 litres of mixture is drawn off and 24 litres of oil is added. If the ratio of paint a… — Answer & Discussion

In a bucket, paint and oil are in the ratio 7 : 5. 24 litres of mixture is drawn off and 24 litres of oil is added. If the ratio of paint and oil becomes 1 : 1, then how many litres of paint was contained in the bucket initially?

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Discussion 1

CCommunity26 Apr 2019

Let initial quantity of paint and oil be 7x and 5x

⇒ Total quantity = 7x + 5x = 12x

Now 24 litres is removed and 24 litres oil is added

⇒ Quantity of paint left = 7x – {24 × (7x/12x)} = 7x – 14

⇒ Quantity of oil = 5x – {24 × (5x/12x)} + 24 = 5x – 10 + 24 = 5x + 14

According to question,

⇒ (7x – 14) / (5x + 14) = 1/1

⇒ 7x – 14 = 5x + 14

⇒ 2x = 28

⇒ x = 14

∴ initial quantity of paint = 7x = 7 × 14 = 98 litres