A 40-liter mixture contains juice and water in the ratio 5:3. How much water (in liters) must be added to this mixture to change the ratio of juice to water to 2:3?

Correct — B. Adding water leaves the juice fixed, so find the juice first.

Juice = 40 × 5⁄8 = 25 L
Water now = 40 × 3⁄8 = 15 L

Target juice : water = 2 : 3, so water = 25 × 3⁄2 = 37.5 L
Water to add = 37.5 − 15 = 22.5 L → option (b).

Why the others are wrong

• (a)
  15.5 litres — Water becomes 15 + 15.5 = 30.5 L, so juice : water = 25 : 30.5 = 50 : 61. That is still far richer in juice than 2 : 3.
• (c)
  25 litres — Water becomes 15 + 25 = 40 L, so juice : water = 25 : 40 = 5 : 8, not 2 : 3. The 25 is the juice already in the mixture, not the water to add.
• (d)
  30 litres — Water becomes 15 + 30 = 45 L, so juice : water = 25 : 45 = 5 : 9 — too much water. The 2 : 3 target needs exactly 37.5 L of water in total.

When only one component is added, the other component is the anchor. The juice stays at 25 L however much water goes in.

Scale the new ratio to that anchor: 2 parts juice = 25 L, so 1 part = 12.5 L and 3 parts water = 37.5 L.

Subtract the 15 L of water already present to get the amount to add.

Key facts

• 40 L in the ratio 5 : 3 holds 25 L of juice and 15 L of water.
• Adding water changes the ratio but not the quantity of juice.
• Water needed for 2 : 3 = 25 × 3⁄2 = 37.5 L, so 22.5 L is added.

Common traps

• Reading the new ratio as water : juice, which gives water = 25 × 2⁄3 ≈ 16.7 L and only about 1.7 L to add.
• Scaling the new ratio to the whole mixture instead of to the fixed 25 L of juice.
• Stopping at 37.5 L, the total water needed, and forgetting to subtract the 15 L already there.

No directly related past PYQ was found.