a certain sum at simple interest becomes rs.5600 in 2 year and rs.6500 in 5 year find the principal and rate of interest p.a •
Answers
The principal is Rs. 5000 and the rate of interest is 6% p.a.
Explanation:
Formula Used:
- Simple interest, S.I. = Amount – Principal = [PRT] / 100
Let the principal be denoted as “P” and the rate of interest be denoted as “R”%.
According to the question and based on the formula we can write the eq. as,
Equation 1:
5600 – P = [PR*2]/100
⇒ 560000 – 100P = 2PR
⇒ [280000 – 50P] = PR …… (i)
Equation 2:
6500 – P = [PR*5]/100
⇒ 650000 – 100P = 5PR
⇒ [650000 – 100P] = 5*[280000 – 50P] …… [substituting from (i)]
⇒ [650000 – 100P] = 1400000 – 250P
⇒ 250P – 100P = 1400000 – 650000
⇒ 150P = 750000
⇒ P = Rs. 5000 ← the principal
Substituting the value of P in eq. (i), we get
[280000 – 50P] = PR
⇒ [280000 – (50*5000)] = 5000*R
⇒ 280000 – 250000 = 5000R
⇒ 5000R = 30000
⇒ R = 6% p.a. ← the rate of interest
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