In a mixture of 110 litre the ratio of water and milk is 4:7 respectively. How much water must be added to make the ratio of water and milk as 8: 7 respectively?

Correct option is C

Given:
Initial ratio of water to milk = 4:7
Total quantity of the mixture = 110 litres
Formula Used:
Amount of water = (Ratio of water / Total ratio) × Total mixture
Amount of milk = (Ratio of milk / Total ratio) × Total mixture
Solution:
Initially, the ratio of water to milk is 4:7, so total ratio = 4 + 7 = 11 parts.
Amount of water = (4/11) × 110 = 40 litres
Amount of milk = (7/11) × 110 = 70 litres
Let x litres of water be added to the mixture.
The new amount of water will be 40 + x litres, and the amount of milk remains 70 litres.
The new ratio of water to milk is 8:7, so:
(40 + x) / 70 = 8/7
Cross-multiply to solve for x:
7 × (40 + x) = 8 × 70
280 + 7x = 560
7x = 560 - 280 = 280
x = 280 / 7 = 40 litres
Thus, 40 litres of water must be added to make the ratio 8:7.