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Question

Answers

A. 4 months

B. 5 months

C. 6 months

D. 8 months

Answer

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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.

__Complete step-by-step answer:__

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.

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.

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