What is the rate of simple interest per annum, when the interest of some money in 10 years will be \frac{2}{5} part of its amount?
WBBSE
Class X
Mathematics
Simple Interest
02 Mark
2022
Given: In 10 years, interest = \frac{2}{5} of the amount.
Let principal = P, rate = r% p.a., interest in 10 years = I.
Relation with amount:
I = \frac{2}{5}(P + I)
⇒ 5I = 2P + 2I
⇒ 3I = 2P
⇒ I = \frac{2}{3}P
Simple interest formula for 10 years:
I = P × r × 10 / 100
So, P × r × 10 / 100 = \frac{2}{3}P
⇒ r × 10 / 100 = \frac{2}{3}
⇒ r = \frac{2}{3}\times \frac{100}{10}=\frac{20}{3}
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