In a mixture of milk and water, the proportion of water by weight was 75%. If in the 60 gms mixture 15 gm of water was added, what would be the percentage of water?

### Concept & Formula This involves a **Simple Mixture Addition**. We must calculate the initial quantities of the components, add the new volume to the specific component (water), and then find the new percentage over the updated total weight. $$ \text{New Percentage} = \left( \frac{\text{Initial Water} + \text{Added Water}}{\text{Initial Total} + \text{Added Mixture}} \right) \times 100 $$ ### Step-by-Step Solution * **Given:** * Initial mixture weight = $60$ gms * Initial proportion of water = $75\%$ * Water added = $15$ gm * **Calculation:** * Initial water quantity = $75\%$ of $60 = \frac{3}{4} \times 60 = 45$ gms. * New water quantity after adding $15$ gm = $45 + 15 = 60$ gms. * New total weight of the mixture = $60$ (initial) $+ 15$ (added) $= 75$ gms. * New percentage of water = $\left(\frac{60}{75}\right) \times 100$. * Simplifying the fraction: $\frac{60}{75} = \frac{4}{5}$. * $\frac{4}{5} \times 100 = 80\%$. * The exact new percentage of water is $80\%$, which does not appear in options (a), (b), (c), or (d). ### Exam Strategy & Shortcut **Fractional Method:** Calculate initial water rapidly: $\frac{3}{4} \times 60 = 45$ gms. Add $15$ gms water: new water = $60$, new total = $75$. Fraction = $\frac{60}{75}$. Recognize immediately that both are divisible by $15$. $\frac{4}{5} = 80\%$. Instantly spot that $80\%$ is missing from the numerical options, so 'None of these' is the correct choice. Don't second guess your calculation if the math is clean. ### Common Pitfall A classic mistake is calculating the new water amount ($60$ gms) but forgetting to add the $15$ gms to the *total mixture weight* denominator. This leads to an incorrect calculation of $\frac{60}{60} = 100\%$, which is strategically placed as trap option (d). ### Final Answer **Therefore, the correct answer is None of these.**