Krishnamurthy started a business investing Rs. 6000. Three months later Madhavan joined him investing Rs. 4000. If they make a profit of Rs. 5100 at the end of the year, how much should be Madhavan’s share?
A. Rs.1700
B. Rs.1400
C. Rs.1300
D. Rs.1732.75

Hint: We will find the ratio of profit earned by Krishnamurthy and Madhavan by writing it as the ratio of the product of money invested and the time for which the money was invested. Simplify it and then the common factor of the ratio be $x$. Add the profit earned by Krishnamurthy and Madhavan and equate it to Rs. 5100 to find the value of the common factor. Further, determine the Madhavans share.

Complete step by step Answer:

We are given that the investment by Krishnamurthy is 6000 and he invested the amount for 1 year. Then, Madhavan invested Rs. 4000 after 3 months. That is, Madhavan invested for 9 months.
The ratio of the profit is equal to the ratio of product of money invested and the time for which the money was invested.
We will calculate the ratio of the profit earned by Krishnamurthy and Madhavan by finding the ratio of product of money invested and the time for which the money was invested.
Here, the product of investment and the time of Krishnamurthy is $6000 \times 12$ and the product of investment and the time of Madhavan is $4000 \times 9$
Hence, the ratio of profit is written as $6000 \times 12:4000 \times 9$
We know that the ratio $a:b$ can also be written as $\dfrac{a}{b}$
Now, we will simplify the above expression as,
$\dfrac{{6000 \times 12}}{{4000 \times 9}} = \dfrac{{72}}{{36}} = \dfrac{2}{1}$
Hence, the ratio of profit is $2:1$
Let the common factor of ratio be $x$
Then, the profit earned by Krishnamurthy is $2x$ and the profit earned by Madhavan is $x$.
Then, the total profit earned is $x + 2x = 3x$
But, we are given that the total profit earned is Rs.5100
This implies
 $
  3x = 5100 \\
  x = 1700 \\
 $
We have to find the Madhavans share, and his share is $x$ which is equal to Rs.1700
Hence, option (A) is the correct answer.

Note: The ratio of the amount of profit earned will be the ratio of the money invested if the time is equal for both the investments. But, if the time is not the same then the ratio of the amount of profit earned will be the ratio of the product of money invested and the time for which money is invested.