A 60-litres solution of alcohol and water has 20% water. How many litres of alcohol must be added to the solution to make the water content 15%?

Correct — B. Adding alcohol leaves the water unchanged, so track the water.

Water now = 20% of 60 = 12 litres
After x litres of alcohol go in, those 12 litres must be 15% of the total.
New total = 12 ÷ 0.15 = 80 litres
Alcohol to add = 80 − 60 = 20 litres → option (b).

Why the others are wrong

• (a)
  10 litres — With 10 litres added the total is 70, and 12 ÷ 70 ≈ 17.14% water — still above the 15% target.
• (c)
  30 litres — With 30 litres added the total is 90, and 12 ÷ 90 ≈ 13.33% water, which dilutes the water below 15%.
• (d)
  40 litres — With 40 litres added the total is 100 and the water 12 litres, which is 12% — too dilute for a 15% target.

When only one component is added, the other component's quantity is fixed, and it anchors the calculation.

The water stays at 12 litres, so its share can fall from 20% to 15% only if the total grows. 12 litres is 15% of 80 litres, so 20 litres must go in.

The same check in ratio form: alcohol : water goes from 48 : 12 to 68 : 12, and 12 ÷ 80 = 15%.

Key facts

• The original 60 litres hold 12 litres of water and 48 litres of alcohol.
• New total = unchanged quantity ÷ its new fraction = 12 ÷ 0.15 = 80 litres.
• The final solution holds 68 litres of alcohol and 12 litres of water.

Common traps

• Taking 15% of the original 60 litres, 9 litres, as the new water content, although no water is removed.

No directly related past PYQ was found.