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Arjun, Sid and Varun invested Rs. 60000, Rs. 50000 and Rs. 40000 in a business respectively. After 4 months, Sid withdrew Rs. 20000, while Varun invested Rs. 10000 more. After 3 more months, Arjun also withdrew some money. At the end of the year, if Arjun received Rs. 31368 as his share in the profit of Rs. 80000, how much money did he withdraw?

Arjun, Sid and Varun invested Rs. 60000, Rs. 50000 and Rs. 40000 in a business respectively. After 4 months, Sid withdrew Rs. 20000, while Varun invested Rs. 10000 more. After 3 more months, Arjun also withdrew some money. At the end of the year, if Arjun received Rs. 31368 as his share in the profit of Rs. 80000, how much money did he withdraw? Correct Answer Rs. 15000

Let Arjun withdrew Rs. ‘x’

Arjun’s investment = 60000 × (4 + 3) + (60000 - x) × (12 - 4 - 3) = 420000 + 300000 - 5x = 720000 - 5x

Sid’s investment = 50000 × 4 + (50000 - 20000) × (12 - 4) = 200000 + 240000 = 440000

Varun’s investment = 40000 × 4 + (40000 + 10000) × (12 - 4) = 160000 + 400000 = 560000

Now, ratio of their investments = (720000 - 5x) ∶ 440000 ∶ 560000 = (72 - 5x/10000) ∶ 44 ∶ 56

Sum of ratios = 72 - 5x/10000 + 44 + 56 = 172 - 5x/10000

As we know, ratio of their investments = ratio of their shares in profit

Hence, Arjun’s share = (72 - 5x/10000)/(172 - 5x/10000) = 31368/80000

⇒ 5760000 - 40x = 5395296 - 15.684x

⇒ 24.316x = 364704

⇒ x = 14998.5 ≅ 15000

∴ Arjun withdrew Rs. 15000

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