Question

A man buys spirit at Rs. 60 per litre, adds water to it and then sells it at Rs. 75 per litre. What is the ratio of spirit to water if his profit in the deal is 37.5%?

• A. $9 : 1$
• B. $10 : 1$
• C. $11 : 1$
• D. None of these

Hint:

In mixture problems with profit percentage given, equate total selling price to total cost price plus profit, then solve for the quantities.

Answer 1

The Correct Option is A

Let the quantity of spirit be $S$ litres and the quantity of water be $W$ litres.
Since water costs nothing, the cost price of the mixture = Cost of spirit only = $60 \times S$.
Selling price per litre = Rs. 75. Total selling price = $75 \times (S + W)$.
We are told that profit = 37.5% = $\frac{3}{8}$ of cost price.
So: \[ \text{Selling Price} = \text{Cost Price} + \text{Profit} = 60S + \frac{3}{8} \times 60S. \] Simplify profit term: $\frac{3}{8} \times 60S = 22.5S$.
Thus, Selling Price = $(60S + 22.5S) = 82.5S$.
But also, Selling Price = $75(S + W)$.
Equating: $75(S + W) = 82.5S$.
Divide through by 75: $S + W = 1.1S$.
So: $W = 0.1S$.
Therefore, the ratio $S : W = S : 0.1S = 10 : 1$. Wait — this gives 10:1, but the options say 9:1 is correct in (A). Let's recheck profit calculation.
Given profit is 37.5%, that is $\frac{3}{8}$ of cost price: \[ \frac{\text{SP} - \text{CP}}{\text{CP}} = \frac{3}{8}. \] So: $\text{SP} = \frac{11}{8} \times \text{CP}$.
Here, CP = Rs. 60 per litre $\times$ $S$ litres = $60S$.
So: $\text{SP} = \frac{11}{8} \times 60S = 82.5S$ (same as before).
Equate to $75(S + W)$: $75(S + W) = 82.5S \Rightarrow S + W = 1.1S \Rightarrow W = 0.1S$.
Thus, $S : W = 10 : 1$, which matches option (B), not (A).
Therefore, the correct ratio is $\boxed{10 : 1}$.