The ratio of water and milk in a mixture of 65 litre is 5 : 8. What quantity of water(in litre) must be added so that the ratio of water and milk becomes 3: 4?

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RRB NTPC Exam 27 Jan 2021 click here to view all questions

The ratio of water and milk in a mixture of 65 litre is 5 : 8. What quantity of water(in litre) must be added so that the ratio of water and milk becomes 3: 4?

A3 litres

B4 litres

C5 litres

D6 litres

Akhilesh ? Apr 1 '25 at 20:29

correct answer is: option c [5 litres]
Explanation: Initially, the mixture has 65 litres with a water to milk ratio of 5:8. First, determine the initial quantities of water and milk.
Let the initial quantity of water be \(5x\) litres and the initial quantity of milk be \(8x\) litres. Therefore, \(5x + 8x = 65\).
This simplifies to \(13x = 65\), so \(x = 5\).
Initial quantity of water = \(5 \times 5 = 25\) litres.
Initial quantity of milk = \(8 \times 5 = 40\) litres.
Let the quantity of water to be added be \(y\) litres. The new quantity of water becomes \(25 + y\) litres, while the quantity of milk remains 40 litres.
The new ratio of water to milk is 3:4. Thus, \(\frac{25 + y}{40} = \frac{3}{4}\).
Cross-multiplying gives \(4(25 + y) = 3 \times 40\), which simplifies to \(100 + 4y = 120\).
Therefore, \(4y = 20\), and \(y = 5\).
So, 5 litres of water must be added

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correct answer is: option c [5 litres] Explanation: Initially, the mixture has 65 litres with a water to milk ratio of 5:8. First, determine the initial quantities of water and milk. Let the initial quantity of water be \(5x\) litres and the initial quantity of milk be \(8x\) litres. Therefore, \(5x + 8x = 65\). This simplifies to \(13x = 65\), so \(x = 5\). Initial quantity of water = \(5 \times 5 = 25\) litres. Initial quantity of milk = \(8 \times 5 = 40\) litres. Let the quantity of water to be added be \(y\) litres. The new quantity of water becomes \(25 + y\) litres, while the quantity of milk remains 40 litres. The new ratio of water to milk is 3:4. Thus, \(\frac{25 + y}{40} = \frac{3}{4}\). Cross-multiplying gives \(4(25 + y) = 3 \times 40\), which simplifies to \(100 + 4y = 120\). Therefore, \(4y = 20\), and \(y = 5\). So, 5 litres of water must be added Akhilesh ? answered Apr 1 '25 at 20:29

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