What percent of water must be mixed with honey so as to gain 20% by selling the mixture at the cost price of honey?

Correct Option: (a) 20%

Let the cost price (CP) of 1 litre of pure honey be ₹ 100. To gain 20% by selling the mixture of honey and water at the cost price of honey, the Selling Price (SP) of 1 litre of the mixture must be ₹ 100. Since the seller makes a 20% profit, the cost price of 1 litre of this mixture must be: CP of mixture = SP / (1 + Profit%) = 100 / 1.20 = ₹ 250 / 3. Let H and W be the volume of honey and water mixed together. Since water is free, its CP is ₹ 0. Using the weighted average formula for the mixture: CP of mixture = (H × CP of honey + W × CP of water) / (H + W) ⇒ 250 / 3 = (H × 100 + W × 0) / (H + W) ⇒ 250(H + W) = 300H ⇒ 250W = 50H ⇒ W / H = 50 / 250 = 1 / 5. The volume of water mixed is 1/5th of the volume of honey. To find the percentage of water mixed with honey: Percentage of water = (W / H) × 100% = (1 / 5) × 100% = 20%. Thus, 20% of water must be mixed. The correct option is (a).