Ramesh borrowed from Suresh certain sum for 2 years at simple interest. He lent this 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.
Answers
Answer:
simple interest formula is = P × R ×T / 100
Answer:
hola mate
Step-by-step explanation:
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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