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

• Let the cost price (CP) of 100 units of pure honey be 100.

• To gain 20% by selling the mixture at the CP of honey, the selling price (SP) of the mixture must be 120.

• Since the mixture is sold at the CP of honey, the SP per unit of the mixture is the same as the CP per unit of honey.

• Let the quantity of honey in the mixture be $H$ and water be $W$. The total quantity is $H + W$.

• The cost of the mixture is only the cost of honey, which is $H \times \text{CP}_{\text{honey}}$.

• The selling price is $(H + W) \times \text{CP}_{\text{honey}}$.

• For a 20% gain, $\text{SP} = 1.20 \times \text{CP}_{\text{mixture}}$. Thus, $(H + W) \times \text{CP}_{\text{honey}} = 1.20 \times H \times \text{CP}_{\text{honey}}$.

• Simplifying, $H + W = 1.20 H$, which means $W = 0.20 H$.

• The percentage of water in the mixture is $\frac{W}{H + W} \times 100 = \frac{0.20 H}{1.20 H} \times 100 = \frac{1}{6} \times 100 \approx 16.67\%$. Wait, let me re-read the question carefully. 'What percent of water must be mixed with honey'. This usually implies the ratio of water to honey or water to total mixture? In UPSC CSAT, 'percent of water mixed with honey' often refers to the proportion of water in the final mixture or the amount added relative to the honey. Let's check the options. 20, 10, 5, 4. My calculation of 16.67% is not an option. Let's re-evaluate the interpretation.

• Alternative interpretation: 'Gain 20% by selling the mixture at the cost price of honey'. This means the profit is 20% of the *cost of the mixture*? Or 20% of the *cost of the honey*? Standard profit/loss is on cost price. Cost price of mixture = Cost of honey. Selling price = Price of honey per unit * Total volume. Profit = SP - CP. Gain % = (Profit / CP) * 100. So (SP - CP)/CP = 0.20. SP = 1.20 CP. This leads to the same equation: Volume_mixture * Price_honey = 1.20 * Volume_honey * Price_honey. So Volume_mixture = 1.20 Volume_honey. Water = 0.20 Volume_honey. The question asks 'What percent of water must be mixed with honey'. This phrasing is ambiguous. Does it mean (Water/Honey)*100 or (Water/Total)*100? If it means Water/Honey, then 20%. If it means Water/Total, then 16.67%. Since 20% is an option and 16.67% is not, the question asks for the percentage of water relative to the honey used, i.e., the ratio of water to honey expressed as a percentage.

• Therefore, Water = 20% of Honey.

• The key option (a) 20% follows from the ratio of water to honey being 1:5, which is 20%.