A, B and C invest in a business for the same period. A invests \(\frac{3}{8}\) of the total capital and B invests \(\frac{1}{3}\) of the total capital; C invests the rest. Find the ratio A : B : C of their profits.
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 9 : 8 : 7
The money stays in for the same period, so the profit is shared in the ratio of the capitals. C’s part is what is left of the whole capital.
C’s part \(\displaystyle =1-\frac{3}{8}-\frac{1}{3}=\frac{24-9-8}{24}=\frac{7}{24}\)
A : B : C \(\displaystyle =\frac{9}{24}:\frac{8}{24}:\frac{7}{24}\)
Multiplying by 24 gives \(9:8:7\)
The profits are in the ratio A : B : C = 9 : 8 : 7.
Why the other options are incorrect
Option (1) 1 : 4 : 5 — Incorrect. It gives A the smallest share, although A has the largest part of the capital, \(\frac{9}{24}\).
Option (3) 8 : 7 : 9 — Incorrect. It gives C the largest share, but C has only \(\frac{7}{24}\), the smallest part.
Option (4) 7 : 8 : 9 — Incorrect. This is the right ratio the wrong way round, C : B : A instead of A : B : C.