Question

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

Answer 1

Hint: Assume a variable t which represents the time in years after which the amounts of debts of A and B becomes equal. In simple interest, we have a formula to calculate the amount after t years for a principal amount p at a rate of interest r per annum simple interest. This formula is amount = $p+{\displaystyle \frac{p\times r\times t}{100}}$ . Use this formula to get an equation in t which can be solved to get the value of t.

Complete step-by-step answer:
Before proceeding with the question, we must know all the formulas that will be required to solve this question.
For a principal amount Rs p at a rate of interest r per annum simple interest, the amount after t years is given by the formula,
Amount = $p+{\displaystyle \frac{p\times r\times t}{100}}.............\left(1\right)$
In the question, A borrows Rs 8000 at 12% per annum simple interest and B borrows Rs 9100 at 10% per annum simple interest. We are required to find the number of years after which their amounts become equal.
Let us assume that after t years, their amounts become equal.
Since A borrows Rs 8000 at 12% per annum simple interest, using formula $\left(1\right)$, the amount after t years is equal to,
$$\begin{array}{rl}& 8000+{\displaystyle \frac{8000\times 12\times t}{100}}\\ & \Rightarrow 8000+960t.............\left(2\right)\end{array}$$
Since B borrows Rs 9100 at 10% per annum simple interest, using formula $\left(2\right)$, the amount after t years is equal to,
$$\begin{array}{rl}& 9100+{\displaystyle \frac{9100\times 10\times t}{100}}\\ & \Rightarrow 9100+910t.............\left(3\right)\end{array}$$
Since the amounts we got in $\left(2\right)$ and $\left(3\right)$ are equal, we get,
$$\begin{array}{rl}& 8000+960t=9100+910t\\ & \Rightarrow 50t=1100\\ & \Rightarrow t=22\end{array}$$
Hence, the answer is 22 years.

Note: There is a possibility that one may commit a mistake while applying the formula for the amount. It is a very common mistake that one forgets to divide $p\times r\times t$ term by 100 in the formula we used to calculate the amount and this mistake may lead us to an incorrect answer.