We want to figure out an easy way of solving Simple Interest problems in which the amounts after ‘a’ and ‘b’ years respectively are given and you are asked about the Principal Amount and Rate of Simple Interest. You are given four pieces of data:I. No. of Years ‘a’II. Amount after ‘a’ yearsIII. No. of Years ‘b’IV. Amount after ‘b’ years
Obviously, to solve this kind of problem, we should know the basics of simple interest.
We usually apply simple interest formula to solve these kinds of questions, form equations, solve them at the same time to find principal amount and simple interest and then apply another simple interest formula to find the rate of interest. However, there is an easier and quicker method.
We know that the simple interest remains the same for any year. Using this concept, we try to solve the problem visually.
Here is a sample question.
Question:- A sum of money at SI amounts to Rs. 550 in 5 years and Rs. 600 in 6 years. What is the Principal and the Rate of Interest?
Solution: We know that simple interest is same for all the years. So we find the difference in the number of years and the amounts.
The difference in number of years = 6 – 5 = 1 year
The difference in amounts = Rs. 600 – Rs. 550 = Rs. 50
∴ Simple Interest = Rs. 50/ 1 year = Rs. 50/ year
∴ SI for 6 years = 50 × 6 = 300
Principal Amount = Amount after 6 years – SI for 6 years
Now you saw how we solved this question without using basic simple interest formula i.e. p*r*t/100 and then further on. You must be speedy in calculation so you could save more time. This problem could have easily been solved in your head using this method without writing down a single equation. This could save you at least 45 seconds per question.
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