 QUESTION

# Person A begins a business with Rs. 85,000. He was joined afterwards by B with Rs. 42,500. For how much period does B join, if the profit at the end of the year is divided in the ratio of 3 : 1 ?A. 4 monthsB. 5 monthsC. 6 monthsD. 8 months

Hint: We have to only use simple interest formula i.e. $S.I. = \dfrac{{PRT}}{{100}}$ (where SI is simple interest, P is principal mount, R is the rate of interest and T is the time period) and divide them to get their ratio.

As we know that the B has joined afterwards A.
And person A joined for 12 months.
So, let person B join for x months.
To apply a simple interest formula, we had to also assume rate of interest as r%.
But the rate of interest should be the same for both of the persons.
Now, simple interest of person A for 12 months will be $\dfrac{{85000 \times r \times 12}}{{100}} = 10200r$
And the simple interest of person B for x months will be $\dfrac{{42500 \times r \times x}}{{100}} = 425rx$
Now, as we know that the simple interest of person A and person B is in ratio of 3 : 1.
So, $\dfrac{{10200r}}{{425rx}} = \dfrac{3}{1}$
$\dfrac{{10200}}{{425x}} = \dfrac{3}{1}$
Now cross multiplying the above equation to find the value of x. We get,
10200 = 1275x
Dividing both sides of the equation by 1275. We get,
$x = \dfrac{{10200}}{{1275}} = 8$
So, person B joined for a period of 8 months.
Hence, the correct option will be D.

Note: Whenever we come up with this type of problem then first, we had to assume the time period of person B as x months and then we had to assume rate of interest as r%. But the rate of interest should be the same for both the persons. After that we can apply a simple interest formula to calculate the interest of person A for 12 months and interest of person B for x months. After that we divide their interest and equate that with the given ration. After solving that equation. We will get the required value of x.