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.**