Question

Ramesh borrowed from Suresh certain sum for 2 years at simple interest ,and lent the sum to Dinesh at the same rate for 2 years compound interest . at the end of 2 years Ramesh received 110 as compound interest from dinesh but paid 100 as simple interest to Suresh. find the sum and the rate of interest.​

Answer 1

The sum is Rs. 250 and the rate of interest is 20%.

Step-by-step explanation:

Required formula:

• Simple Interest, S.I. = $\frac{PRT}{100}$

• Compound Interest, C.I. = P [(1 + $\frac{R}{100}$ )ⁿ - 1]

Let the sum of money for both the cases be Rs. “P” and the rate of interest be “R”% p.a..

Time period, T or n = 2 years

S.I. = Rs. 100

C.I. = Rs. 110

It is given that Ramesh borrowed the sum from Suresh at simple interest for 2 years, so, based on the first formula above and substituting the given values, we can write the equation as,

100 = $\frac{PR * 2}{100}$

⇒ PR = $\frac{100 * 100}{2}$

⇒ P = $\frac{5000}{R}$ ...... (i)

Now, it is also given that Ramesh lent the same sum of money to Dinesh at the same rate of interest for 2 years compound interest, so based on the second formula above and substituting the given values, we can write the equation as,  

110 = P [(1 + $\frac{R}{100}$ )² - 1]

⇒ 110 = $\frac{5000}{R}$ [(1 + $\frac{R}{100}$ )² - 1] ....... [substituting from (i)]

⇒ 11 = $\frac{500}{R} [1 + \frac{2R}{100} + \frac{R^2}{100^2}] - \frac{500}{R}$

⇒ 11 = $\frac{500}{R} + 10 + \frac{R}{20} - \frac{500}{R}$

⇒ 11 - 10 = $\frac{R}{20}$

⇒ R = 20% ← the rate of interest

Substituting the value of R in eq. (i), we get

P = $\frac{5000}{R}$

⇒ P = $\frac{5000}{20}$

⇒ P = Rs. 250 ← the sum of money

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