700 ml of a mixture contains water and milk in the ratio 2 ∶ 8. How much water must be added to the mixture so that the ratio of water and milk becomes 3 âˆ¶ 8 ?

Given:

Mixture volume = 700 ml

Ratio of water to milk = 2:8

Concept:

We need to adjust the volume of water to change the ratio to 3:8.

Calculation:

Initial volumes:

⇒ Volume of water = (2/10) × 700 ml = 140 ml

⇒ Volume of milk = (8/10) × 700 ml = 560 ml

Let x be the amount of water to be added.

New volume of water = 140 ml + x

New ratio of water to milk = (140 + x) : 560

We want this new ratio to be 3:8:

⇒ (140 + x) / 560 = 3 / 8

Solving for x:

⇒ 8(140 + x) = 3 × 560

⇒ 1120 + 8x = 1680

⇒ 8x = 560

⇒ x = 70

∴ The amount of water to be added is 70 ml.