Question

Musa and Akiola together invest $52,000 in a business and agree to share the profit in the ratio of their investment. Musa receives $5,000 and Akiola receives $8,000 as a profit at the end of the first year. How much did each invest?

Answer 1

Money invested by Musa and Akiola together in a buisness=$52,000

Profit earned by Musa =$5,000

Profit earned by Akiola=$8,000

Ratio of profit earned by Musa to the profit earned by Akiola:-

$= 5000 : 8000$

Now, let us simplify the ratio of their profits:-

$= 5000 : 8000$

$= \frac{5000}{8000}$

$= \frac{5000 \div 1000}{8000 \div 1000}$

$= \frac{5}{8}$

$= \bold{ 5 : 8}$

Thus, the ratio of profit earned by Musa to the profit earned by Akiola=5:8

It is given that :-

The ratio of profit earned by Musa to the profit earned by Akiola=The ratio of money invested by Musa to the money invested by Akiola

Which means :-

The ratio of money invested by Musa to the money invested by Akiola=5:8

Then :-

Money invested by Musa :-

$= \frac{5}{5 + 8} \: \: of \: \: 52000$

$= \frac{5}{13} \: \: of \: \: 52000$

$= \frac{5}{13} \times 52000$

$= \frac{5 \times 52000}{13}$

$= \frac{260000}{13}$

$= \bold{\ \: 20,000}$

Thus, the money invested by Musa =$20,000

Money invested by Akiola:-

$= \frac{8}{5 + 8} \: \: of \: \: 52000$

$= \frac{8}{13} \: \: of \: \: 52000$

$= \frac{8}{13} \times 52000$

$= \frac{8 \times 52000}{13}$

$= \frac{416000}{13}$

$= \bold{ \ \: 32,000}$

Thus, the money invested by Akiola =$32,000

As the sum of their investments add up to form $52,000 we can conclude that we have found out the correct amount of money each of them invested in the business.

Therefore, the money invested by Musa in the buisness =$20,000 and the money invested by Akiola in the buisness=$32,000