Question

A bonus of £2100 is shared by 10 people who work for a company. 40 percent of the bonus is shared equally between 3 managers. The rest of the bonus is shared equally between 7 salesmen. One of the salesmen say if the bonus is shared equally between all 10 people I will get 25 percent more money. Is the salesmen correct? you must show your answer.

Help me on this question and please show your working out and explain thank you

Answer 1

Salesman is not correct

Explanation:

First we calculate the share of salesman when 60 percent of bonus is shared among 7 salesmen:

Bonus Share For 7 Salesmen = (0.6)(£ 2100)

Bonus Share For 7 Salesmen = £ 1260

Now, this is equally divided among 7 salesmen:

Bonus Share of 1 Salesmen (when 60% is shared) = S₁ = £ 1260/7

S₁ = £ 180

Now, we calculate the share each salesmen get if bonus is equally divided among 10 people:

Bonus Share of 1 Salesmen (when equally shared) = S₂ = £ 2100/10

S₂ = £ 210

S₂/S₁ = £ 210/£ 180

S₂/S₁ = 1.16

S₂ = 1.16S₁

S₂ = 116% of S₁

This means that if bonus is equally divided between all 10 people then the salesman will get 16 percent more money.

Therefore, salesman is not correct