NIMCET 2023 — Reasoning PYQ

Step-by-step Solution 

 

1. Calculate the initial amount of water: The initial mixture is $30\text{ litres}$ and contains $10\%$ water. The amount of water is calculated as $30\text{ litres}\times \frac{10}{100}=3\text{ litres}$. 

2. Calculate the initial amount of milk: The initial amount of milk is found by subtracting the water from the total mixture: $30\text{ litres}-3\text{ litres}=27\text{ litres}$. 

3. Define the new total volume: Let $x$ be the amount of milk added. The new total volume of the mixture will be $30\text{ litres}+x$. 

4. Set up the equation for the new percentage of water: The amount of water remains constant at $3\text{ litres}$. In the new mixture, the water should be $2\%$ of the total volume. This can be expressed as $\frac{3}{30+x}=\frac{2}{100}$. 

5. Solve for $x$: 

• Cross-multiplication is performed: $3\times 100=2\times (30+x)$. 

• This simplifies to $300=60+2x$. 

• Subtracting $60$ from both sides gives $240=2x$. 

• Dividing by $2$ yields $x=\frac{240}{2}=120$.