A, B and C investment in a partnership in the ratio of 5 : 6 : 8. The ratio of their profit is 5 : 3 : 12. Find the ratio of time for their investment:

Question: A, B and C investment in a partnership in the ratio of 5 : 6 : 8. The ratio of their profit is 5 : 3 : 12. Find the ratio of time for their investment:

Solution:
Given that,
A, B and C investment ratio = 5 : 6 : 8
A, B and C profit ratio = 5 : 3 : 12

We know that,
Ratio of Investment x Time = Ratio of Profit
To find the ratio of time just divide respective profits ratios by respective investment ratios
So if the profit ratio is P_A : P_B : P_C and the investment ratio is I_A : I_B : I_C then,
Time ratio is found by = (P_A/I_A) : (P_B/I_B) : (P_C/I_C)
= (5/5) : (3/6) : (12/8)

The ratio of time periods for A, B, and C is found by = (5/5) : (3/6) : (12/8)

Multiplying by 2,
The ratio of time periods for A, B, and C is found by = (5 × 2)/5 : (3 × 2)/6 : (12 × 2)/8
= 2 : 1 : 3