40 in the ratio 2: 3 £2000 in the ratio 3: 7 36kg in the ratio 1: 2: 3

a) 16: 24
b)  £600 : £1400
c)  6 : 12 : 18

40 in the ratio 2 : 3 

To split an amount based on ratio 2:3 , first, we need to find the total share.


Find total shares

2+3 = 5

Then we need to find the the amount of 1 share worth 


Find 1 share

5 shares = 40                ← divide by 5 on both sides
÷ 5             ÷ 5 
1 share = 8 

Now that we know one share is 8, we need to find the amount according to the shares allocation, which is 2 and 3 in this question.


Find 2 shares

1 share = 8                    ← multiply by 2 on both sides
x2           x2
2 shares = 16


Find 3 shares

1 share = 8
x3            x3
3 shares = 24

The ratio is 2 : 3. The 40 is therefore the amount split as 16:24


16: 24


£2000 in the ratio 3: 7

To split the £2000 into the ratio 3:7, first, we need to find the total shares.


Find total shares

3 + 7 = 10

Then we find the 1 share worth

Find 1 share

10 shares = £2000              ← divide by 10 on both sides
÷10              ÷10
1 share = £200

Now that we know 1 share is worth £200, we need to find the shares according to the ratio allocation.


Find 3 shares

1 share = £200                    ← multiply 3 on both sides
x3             x3
3 shares = £600


Find 7 shares

1 share = £200                         ← multiply by 7 on both sides
x7            x7
7 shares = £1400

The ratio 3 : 7, the £2000 is spilt into £600 : £1400


£600 : £1400


36 kg into the ratio 1:2:3

To spilt the 36kg, first we find the total number of shares


Find total shares

1 + 2 + 3 = 6

36 kg is split into 6 shares. We need to find the allocation of 1 share.

Find 1 share

6 shares = 36              ← divide by 6 on both sides
÷6             ÷6
1share = 6kg

The allocation of 1 share is 6kg. Now find 2 shares and 3 shares


Find 2 shares

1 share = 6kg                 ← multiply by2 on both sides
x2            x2
2 shares = 12kg


Find 3 shares

1 share = 6 kg            ← multiply by 2 on both sides
x3            x3
3shares = 18kg

The ratio is 1:2:3. 36kg is spilt into 6: 12: 18


6 : 12 : 18