At the same rate of simple interest in percent per annum, if a principal becomes the amount of Rs. 7,100 in 7 years and Rs. 6,200 in 4 years, determine the principal and rate of simple interest in percent per annum.
WBBSE
Class X
Mathematics
Simple Interest
05 Mark
2022
Let Principal = P, rate = r% per annum.
Amount after 7 years = 7,100
⇒ P + I7 = 7,100 —- (i)
Amount after 4 years = 6,200
⇒ P + I4 = 6,200 —- (ii)
Substracting (i) – (ii)
Interest for 3 years (I3) = 7,100 – 6,200 = 900
Interest for 1 years (I1) = 900 ÷ 3 = Rs. 300
Interest for 4 years (I4) = Rs. 300 × 4 = Rs. 1,200
Substituting I4 in equation (ii)
Principal = Amount − Interest = 6,200 − 1,200 = Rs. 5,000
Rate % = \frac{300}{5000} × 100 = 6%
∴ Principal = ₹ 5,000; Rate = 6% p.a.
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