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Adam, Ben and Charles are to share £300 in the ratio 1:4:5

This means that, Adam is to have 1 share, Ben is to have 4 shares and Charles is to have 5 shares.

Thus the total number of shares is 1 + 4 + 5 = 10

Each share is worth £300 ÷ 10 = £30

Adan is to have 1 share - so Adam will get 1 × £30 = £30

Ben is to have 4 shares - so Ben will get 4 × £30 = £120

Charles is to have 5 shares - so Charles will get 5 × £30 = £150

CHECK
£30 + £120 + £150= £300 √

How much should I show to make the method clear?
1 + 4 + 5 = 10
£300 ÷ 10 = £30
Adam    1 × £30 = £30
Ben         4 × £30 = £120
Charles     5 × £30 = £150
CHECK    £30 + £120 + £150 = £300 √

A similar type of question.

The ages of Richard, Susan and Tom are in the ratio 2:3:5.
The total of the ages of these three people is 150.
How old is Susan?

Richard has 2 shares, Susan has 3 shares and Tom has 5 shares.

Thus the total number of shares is 2 + 3 + 5 = 10

Each share is worth 150 ÷ 10 = 15

Richard is to have 2 shares - so Richard's age is 2 × 15 = 30

Susan is to have 3 shares - so Susan's age is 3 × 15 = 45

Tom is to have 5 shares - so Tom's age is 5 × 15 = 75

CHECK
30 + 45 + 75 = 150 √

Answer........... Susan is 45

How much should I show to make the method clear?
2 + 3 + 5 = 10
150 ÷ 10 = 15
Richard    2 × 15 = 30
Susan      3 × 15 = 45
Tom       5 × 15 = 75
CHECK    30 + 45 + 75 = 150 √
Susan is 45

More fully worked examples of share in ratio
together with questions which cover share in ratio
can be found at the following LINK