A bonus of £3150 is shared by 15 people who work for a company. 40% of the bonus is shared equally between 3 managers.
The rest of the bonus is shared equally between 12 salespeople.
One of the salespeople says,
“If the bonus is shared equally between all 15 people I will double the money.
Is the salesperson correct?
You must show how you get your answer.

We have a bonus of £3150

40% is divided between 3 managers, so if

100% = £3150

40% = X

Now we can solve this for X by taking the quotient of these two equations:

(100%/40%) = (£3150/X)

Then:

X = £3150*(40%/100%) = £1260

Then each one of the 3 managers gets:

£1260/3 = £420

Each manager gets £420

The other £3150 - £1260 = £1890

are divided between 12 salespeople, then each one gets:

£1890/13 = £157.5

Each one of the salespersons will get £157.5

Now there is the case where we divide the £3150 evenly between the 15 workers.

We get:

£3150/15 = £210

Each worker gets £210.

Notice that before, each salesperson gets £157.5 and in this case, each salesperson gets £210.

Then the statement:

"If the bonus is shared equally between all 15 people I will double the money."

Is false.