A dishonest milkman fills up his bucket, which is only 4/7th full of milk, with water. He again removes 3 litres of this mixture from the bucket and adds an equal quantity of water. If milk is now 40% of the mixture, then what is the capacity of the bucket?
1). 25 litres
2). 40 litres
3). 15 litres
4). 10 litres
Let the capacity of bucket be X litres
⇒ Quantity of milk = (4/7)X
⇒ Quantity of water = 1 – (4/7)X = (3/7)X
⇒ If 3 litres mixture is removed, remaining mixture = X – 3
⇒ Now quantity of milk = (4/7) × (X – 3)
⇒ If 3 litres water is added, quantity of water = (3/7) × (X – 3) + 3
⇒ (4/7) × (X – 3) = 40% of X
⇒ (4/7)X – 12/7 = (40/100)X
⇒ {(4/7) – (40/100)}X = 12/7
∴ X = 10 litres