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Amit, Akash and Akshay start a business together. Investment made by Amit is Rs. 2,000 more than that of Akash and Rs. 4,000 more than Akshay. Amit and Akash invest for 6 months each and Akshay invests for 8 months. If ratio of profit at the end of the year is 9 ∶ 6 ∶ 4 , then what was the total investment made by them?

Amit, Akash and Akshay start a business together. Investment made by Amit is Rs. 2,000 more than that of Akash and Rs. 4,000 more than Akshay. Amit and Akash invest for 6 months each and Akshay invests for 8 months. If ratio of profit at the end of the year is 9 ∶ 6 ∶ 4 , then what was the total investment made by them? Correct Answer Rs. 12,000

Given:

Investment of Amit = 2000 + investment of Akash = 4000 + investment of Akshay

Investment of Amit for 6 months

Investment of Akash for 6 months

Investment of Akshay for 8 months

Ratio of profit at the end of the year = 9 ∶ 6 ∶ 4

Concept used:

Ratio of product of time and investment = Ratio of profit

Calculation:

Let, investment of Akash be X, then investment of Amit = X + 2000 and investment of Akshay = (X + 2000) – 4000 = X – 2000

Investment of Amit of 1 year = (X + 2000) for 6 months = (X + 2000) × 6

Investment of Akash for 1 year = X for 6 months = X × 6 = 6X

Investment of Akshay for 1 year = (X – 2000) for 8 months = (X – 2000) × 8

Ratio of product of time and investment = Ratio of profit = 9 ∶ 6 ∶ 4

Ratio of profit = (X + 2000) × 6 ∶ 6X ∶ (X – 2000) × 8

⇒ (X + 2000) × 3 ∶ 3X ∶ (X – 2000) × 4

⇒ (3X + 6000) ∶ 3X ∶ (4X – 8000) = 9 ∶ 6 ∶ 4

Taking first two term together, (3X + 6000)/3X = 9/6 = 3/2

⇒ (3X + 6000)/3X = 3/2

⇒ (3X + 6000) × 2 = 3X × 3 = 9X

⇒ 6X + 12000 = 9X

⇒ 9X – 6X = 12000

⇒ 3X = 12000

⇒ X = 12000/3 = 4000

Total investment = (X + 2000) + X + (X – 2000) = 3X = 3 × 4000 = 12000

∴ Total investment = Rs. 12,000

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