A vessel of 160 L is filled with milk and water.70% of milk and 30% of water is taken out of the vessel.It is found out that the vessel is vacated by 55%,then the quantity of milk and water in the original mixture is

Question

Given below are two statements:
Statement I: In order to get a mixture worth 16-5/kg, a grocer needs to mix two varieties of pulses costing 15 and 20 per kg respectively in the ratio 7:3.
Statement II: A merchant has 1000 kg rice, part of which he sells at 8% profit and the rest at 16% profit. He gains 14% on the whole. The quantity of rice sold at 16% profit is 750 kg.
In the light of the above statements, choose the correct answer from the option given below:

Answer 1

Initially, let \( M \) represent the milk quantity and \( W \) the water quantity. We know:

\[ M + W = 160 \]

After retaining 70% of the milk and removing 55% of the mixture:

\[ 0.3M + 0.7W = 0.45 \times 160 = 72 \]

The system of equations is:

\[ M + W = 160 \quad \text{(1)} \]

\[ 0.3M + 0.7W = 72 \quad \text{(2)} \]

Multiply equation (1) by 0.3:

\[ 0.3M + 0.3W = 48 \quad \text{(3)} \]

Subtract equation (3) from equation (2):

\[ (0.3M + 0.7W) - (0.3M + 0.3W) = 72 - 48 \]

\[ 0.4W = 24 \quad \Rightarrow \quad W = 60 \]

Substitute \( W = 60 \) into equation (1):

\[ M + 60 = 160 \quad \Rightarrow \quad M = 100 \]

Therefore, milk is 100 L and water is 60 L.

A vessel of 160 L is filled with milk and water.70% of milk and 30% of water is taken out of the vessel.It is found out that the vessel is vacated by 55%,then the quantity of milk and water in the original mixture is

The Correct Option is A

Solution and Explanation

Top Questions on Mixtures & Alligations

Questions Asked in CMAT exam