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M and N went into partnership for a year. M invests Rs.450 and B invests Rs.300. After 6 months, M removes Rs.150 and N adds Rs.240 after some months. The average profit share of M and N is Rs.1085. The difference between the shares of N and M is Rs.70. Find the time after which N adds Rs.240 to his investment.
1. 7 months
2. 6 months
3. 4 months
4. 11 months
5. 5 months

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Correct Answer - Option 1 : 7 months

Given:

⇒ Total investment of M = 450 × 6 + 300 × 6 = Rs.4500

Let the time after which N adds Rs.100 to his investment be p.

⇒ Total investment of N = 300 × a + 540 × (12 - a) = Rs.(6480 - 240a)

Total profit of M and N = 1085 × 2 = 2170

The difference between the shares of N and M = Rs.70

Solving,

⇒ Profit share of M = Rs.1050

⇒ Profit share of N = Rs.1120

Ratio of their profit shares = 1050 : 1120 = 15 : 16

Then,

⇒ 4500 : (6480 - 240a) = 15 : 16

Solving,

⇒ a = 7

∴ After 7 months, N adds Rs.240 to his investment.

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