Three partners shared the profit in a business in the ratio 5 : 7 : 8. They…
2024
Three partners shared the profit in a business in the ratio 5 : 7 : 8. They had partnered for 14 months, 8 months and 7 months respectively. What was the ratio of their investments?
- A.
5 : 7 : 9
- B.
20 : 49 : 64
- C.
20 : 54 : 64
- D.
16 : 49 : 64
Attempted by 2 students.
Show answer & explanation
Correct answer: B
Key idea: profit shares are proportional to investment × time.
Let the investments be x, y, z for 14, 8 and 7 months respectively.
Then profit ratios = 14x : 8y : 7z = 5 : 7 : 8.
From 14x / 8y = 5 / 7, we get 98x = 40y ⇒ y = 49/20 · x.
From 14x / 7z = 5 / 8, note 14x/7z = 2x/z = 5/8, so 16x = 5z ⇒ z = 16/5 · x.
Hence x : y : z = x : 49/20 x : 16/5 x. Multiply all terms by 20 to clear denominators: 20 : 49 : 64.
Final answer: 20 : 49 : 64