Discussion

Question:

Two jugs A and B contain 50 litres each of milk and water respectively. 10 litres of milk is taken from jug A and poured into jug B. Then, 10 litres of solution from jug B is removed and poured into jug A. Let the quantity (in litres) of water in jug B and milk in jug A be v_b & v_a respectively. Which of the following is true?

Explanation:

Step 1: 10 litres is transferred from A to B.
Since A contains only milk initially, 10 litres of milk will be transferred from A to B.
Hence, quantity of milk and water in A and B will be

Step 2: 10 litres is transferred from B to A.

Now 10 litres out of 60 litres is transferred from B to A.
⇒ Fraction of solution being transferred = 10/60 = 1/6th

B has 10 litres of milk.
∴ Quantity of milk transferred from B to A = 10 × 1/6 = 5/3 litres

B has 50 litres of water.
∴ Quantity of water transferred from B to A = 50 × 1/6 = 25/3 litres

Hence, quantity of milk and water in A and B will be 3

∴ Final quantity of water in jug B (v_b) = 125/3 litres
and, final quantity of milk in jug A (v_a) = 125/3 litres

⇒ v_a = v_b

Note: If this entire process is repeated again, still the quantity of water in jug B will be same as quantity of milk in jug A, while quantity of milk in jug B will be same as quantity of water in jug A.

Hence, option (a).

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