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# A borrows Rs 800 at the rate of 12% per annum simple interest and B borrows Rs 910 at the rate of 10% per annum, simple interest. In how many years will their amounts of debt be equal: (1) 18 years (2) 20 years (3) 22 years (4) 24 years

Simple interest is the interest amount for a particular principal amount of money at some rate of interest.

## Answer: Their debts will be equal in 22 years.

Let's find the number of years in which their amounts of debt will be equal.

**Explanation:**

Let the number of years after which their debt will be equal = t years

We know that Simple Interest is given as,

SI = ( P × R × T ) / 100

Amount after 't' years = Principal + Interest in 't' years

Amount paid by A = 800 + (800× 12 × t) /100

Amount paid by B = 910 + (910 × 10 × t) /100

According to the question,

Amount paid by A = Amount paid by B

Therefore,

800 + (800× 12 × t) /100 = 910 + (910 × 10 × t) /100

800 + 96t = 910 + 91t

5t = 110

t = 22

Hence, after 22 years the amount will be equal.

### Thus, if A borrows Rs 800 at the rate of 12% per annum simple interest and B borrows Rs 910 at the rate of 10% per annum, simple interest, their debts will be equal after 22 years.

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