Question

Person A borrows Rs. 8000 at 12% per annum simple interest and person B borrows Rs. 9100 at 10% per annum simple interest. In how many years will their amounts be equal ?

Answer 1

Hint: Let us use simple interest formula \[\dfrac{{{\text{P*R*T}}}}{{{\text{100}}}}\] to find interest if P is the principal amount, R is rate of interest per annum and T is the time period.

Complete step-by-step answer:
Let after t years amounts of person A and B become equal.

As we know that the interest in T years if P is the principal amount and R is the rate of interest per annum is given by S.I. = \[\dfrac{{{\text{P*R*T}}}}{{{\text{100}}}}\]
So, total interest of amount borrowed by person A after t years will be \[\dfrac{{{\text{8000*12t}}}}{{{\text{100}}}}\] = Rs. 960t.

The initial amount borrowed by person A is Rs. 8000.

So, the total amount of person A after t years will be Rs. (8000 + 960t).

And, total interest of amount borrowed by person B after t years will be

\[\dfrac{{{\text{9100*10t}}}}{{{\text{100}}}}\] = Rs. 910t.

The initial amount borrowed by person B is Rs. 9100.

So, the total amount of person B after t years will be Rs. (9100 + 910t).

Now according to question,

8000 + 960t = 9100 + 910t (1)

Now we had to solve equation 1, to find the value of t.

So, subtracting 8000 + 910t from LHS and RHS of equation 1. We get,

50t = 1100

t = \[\dfrac{{1100}}{{50}}\] = 22 years.

Hence after 22 years the amounts of both person A and B will become equal.

Note: Whenever we come up with this type of problem then first, we had to assume the number of years as t. After that we will use a simple interest formula to find total interest after t years. After that we will add their initial amount to their total interest after t years to get their total amount after t years. Now we had to equate their total amount to get the required value of t.