NIMCET 2023 — Reasoning PYQ

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Question

NIMCET 2023 — Reasoning PYQ

NIMCET | Reasoning | 2023

A vessel contains total 95 litre mixture of milk & water in the ratio of 15 : 4 respectively P litre of mixture taken out from the vessel and 18 litres water added in the remaining mixture, then the new ratio of milk to water becomes 3 : 2, find the value of P?

Choose the correct answer:

Explanation

Step-by-step Solution

1. Initial quantities of milk and water: The total volume of the mixture is $95 L$ , and the ratio of milk to water is $15 : 4$ .

The initial quantity of milk is calculated as $\frac{15}{15 + 4} \times 95 = \frac{15}{19} \times 95 = 15 \times 5 = 75 L$ . The initial quantity of water is calculated as $\frac{4}{15 + 4} \times 95 = \frac{4}{19} \times 95 = 4 \times 5 = 20 L$ .

1. Quantities of milk and water removed: When $P L$ of mixture is taken out, the ratio of milk to water in the removed quantity is also $15 : 4$ .

The quantity of milk removed is $\frac{15}{19} \times P L$ . The quantity of water removed is $\frac{4}{19} \times P L$ .

1. Quantities of milk and water remaining:

The quantity of milk remaining in the vessel is $75 - \frac{15 P}{19} L$ . The quantity of water remaining in the vessel is $20 - \frac{4 P}{19} L$ .

1. Quantities after adding water: $18 L$ of water is added to the remaining mixture.

The new quantity of milk is $75 - \frac{15 P}{19} L$ . The new quantity of water is $20 - \frac{4 P}{19} + 18 = 38 - \frac{4 P}{19} L$ . [1, 2]

1. Formulating the equation based on the new ratio: The new ratio of milk to water is given as $3 : 2$ .

Therefore, $\frac{75 - \frac{15 P}{19}}{38 - \frac{4 P}{19}} = \frac{3}{2}$ .

1. Solving for P:

Cross-multiplication yields $2 \times (75 - \frac{15 P}{19}) = 3 \times (38 - \frac{4 P}{19})$ . This simplifies to $150 - \frac{30 P}{19} = 114 - \frac{12 P}{19}$ . Rearranging the terms, $\frac{30 P}{19} - \frac{12 P}{19} = 150 - 114$ . This results in $\frac{18 P}{19} = 36$ . Solving for $P$ , $P = \frac{36 \times 19}{18} = 2 \times 19 = 38 L$ .
Final Answer
The value of $P$ is $38 L$ .