Solution:

(i) 3, 12, 15

Consider x as the fourth proportional to 3, 12 and 15

3: 12 :: 15: x

We can write it as

3 × x = 12 × 15

So we get

x = (12 × 15)/ 3

x = 60

(ii) 1/3, 1/4, 1/5

Consider x as the fourth proportional to 1/3, 1/4 and 1/5

1/3: 1/4:: 1/5: x

We can write it as

1/3 × x = 1/4 × 1/5

So we get

x = 1/4 × 1/5 × 3/1

x = 3/20

(iii) 1.5, 2.5, 4.5

Consider x as the fourth proportional to 1,5, 2.5 and 4.5

1.5: 2.5 :: 4.5: x

We can write it as

1.5 × x = 2.5 × 4.5

So we get

x = (2.5 × 4.5)/ 1.5

x = 7.5

(iv) 9.6 kg, 7.2 kg, 28.8 kg

Consider x as the fourth proportional to 9.6, 7.2 and 28.8

9.6: 7.2 :: 28.8: x

We can write it as

9.6 × x = 7.2 × 28.8

So we get

x = (7.2 × 28.8)/ 9.6

x = 21.6