Question

A sum was put at simple interest at a certain rate for 2 years. Had it been put at 2% higher rate, it would have fetched Rs 50 more. Find the sum.

Answer 1

Hint: Start by letting the sum of money be Rs. y, i.e., the principal be x and the rate be x%. Calculate the interest in this case using $ I=\dfrac{P\times r\times t}{100} $ . Then calculate the interest in case of 2% higher interest using the same formula but rate of interest is (x+2) %. Calculate the difference in the interests of the two cases and equate the result with Rs. 50. Solve the equation to get the answer.

Complete step-by-step answer:
Before starting with the question, let us know about interest.
Interest in the financial term is the amount that a borrower pays to the lender along with the repayment of the actual principal amount.
Broadly, there are two kinds of interest, first is the simple interest, and the other is the compound interest.
Now, let us start the solution to the above question by letting the sum of money be Rs. y, i.e., the principal be x and the rate be x%. So, if we use the formula $ I=\dfrac{P\times r\times t}{100} $ and calculate the interest for the period of 2 years, we get
 $ I=\dfrac{P\times r\times t}{100}=\dfrac{y\times x\times 2}{100}..........(i) $
Now, when the interest rate is increased by 2%, i.e., the interest rate is (x+2)%, the interest earned would be:
 $ I=\dfrac{P\times r\times t}{100}=\dfrac{y\times \left( x+2 \right)\times 2}{100}..........(ii) $
Now, it is given that in the second case the person would have earned Rs. 50 more, so the difference of the interests must be equal to Rs. 50.
 $ \dfrac{y\times \left( x+2 \right)\times 2}{100}-\dfrac{y\times x\times 2}{100}=50 $
If we take $ \dfrac{2y}{100} $ common from left-hand side of the equation, we get
 $ \dfrac{2y}{100}\left( x+2-x \right)=50 $
 $ \Rightarrow \dfrac{y}{50}\times 2=50 $
 $ \Rightarrow y=\dfrac{50\times 50}{2}=1250 $
Hence, the answer to the above question is Rs. 1250.

Note: Be careful with the calculations and solving part as there is a possibility of making a mistake in the calculations. It is recommended to learn all the basic formulas related to simple as well as compound interests as they are very much useful in the problems related to money exchange. Also, don’t get confused and take the time period t for both the cases to be 1 years, make sure that you take t=2 for each case.