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M, N and O started a business investing Rs. 4000, Rs. 6000 and Rs. 10000 respectively. After some months N left the business and after another 3 months O also left the business. If after 12 months their profit ratio is 8 ∶ 3 ∶ 10, after how many months did N leave?

M, N and O started a business investing Rs. 4000, Rs. 6000 and Rs. 10000 respectively. After some months N left the business and after another 3 months O also left the business. If after 12 months their profit ratio is 8 ∶ 3 ∶ 10, after how many months did N leave? Correct Answer 3

Let, N left after x months.

∴ M invested money for = 12 months

N invested money for = x months

O invested money for = (x + 3) months

∴ weighted ratio of investment of M, N and O

⇒ 4000 × 12 ∶ 6000 × x ∶ 10000 × (x + 3)

⇒ 24 ∶ 3x ∶ (5x + 15)

According to problem,

⇒ 24 ∶ 3x = 8 ∶ 3

⇒ 8/x = 8/3

⇒ x = 3

∴ N left after 3 months.

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