-  Suppose A invested Rs. 14a for 10 months and B invested Rs. 15a for b months. Then,
14a x 10 / 15a x b = 7/6 ⇒ b = 840 / 105 = 8

Hence, B invested the money for 8 months.

To solve this problem, we need to use the concept of the ratio of investments and the ratio of profits.

Let the initial investments of A and B be 14x and 15x, respectively.

Let the time for which A invested be 10 months and the time for which B invested be y months.

Since the profits are in the ratio 7:6, we can assume that the total profit is 13x. Therefore, A's profit would be (7/13) times the total profit and B's profit would be (6/13) times the total profit.

According to the question, A invested for 10 months and B invested for y months. Therefore, the ratio of the time for which they invested their money is 10:y.

We can now use the formula: Profit = (Investment × Time × Rate of Profit)/100

We know that A's profit was (7/13) times the total profit, and B's profit was (6/13) times the total profit. Therefore, we can write the following equations:

(7/13) × 14x × 10 = (6/13) × 15x × y

Simplifying this equation, we get:

y = (140/90) = 28/18 = 14/9 months

Therefore, B invested his money for 14/9 months, which is approximately 1.56 months, or 1 month and 16 days.

Since none of the options match this value, we can round it up to the nearest option, which is 8 months (Option D).

Hence, the correct answer is Option D, i.e., B invested his money for 8 months.

If you think the solution is wrong then please provide your own solution below in the comments section .