Solution:

(i) It is given that

Mixture of milk to water = 45 litres

Ratio of milk to water = 13: 2

Sum of ratio = 13 + 2 = 15

Here the quantity of milk = (45 × 13)/ 15 = 39 litres

Quantity of water = 45 × 2/15 = 6 litres

Consider x litre of water to be added, then water = (6 + x) litres

Here the new ratio = 3: 1

39: (6 + x) = 3: 1

We can write it as

39/ (6 + x) = 3/1

By cross multiplication

39 = 18 + 3x

3x = 39 – 18 = 21

x = 21/3 = 7 litres

Hence, 7 litres of water is to be added to the mixture.

(ii) It is given that

Ratio between boys and girls = 5: 3

Number of pupils = 560

So the sum of ratios = 5 + 3 = 8

We know that

Number of boys = 5/8 × 560 = 350

Number of girls = 3/8 × 560 = 210

Number of new boys admitted = 10

So the total number of boys = 350 + 10 = 360

Consider x as the number of girls admitted

Total number of girls = 210 + x

Based on the condition

360: 210 + x = 3: 2

We can write it as

360/ 210 + x = 3/2

By cross multiplication

630 + 3x = 720

3x = 720 – 630 = 90

So we get

x = 90/3 = 30

Hence, 30 new girls are to be admitted.