11. A sum of money becomes ten times itself at simple
interest. If the time period (in years) is numerically equal
to the rate of interest, find the annual rate of interest.
(A) 25%
(B) 20%
(C) 30%
(D) 90%
Answers
Answer:
30%
Step-by-step explanation:
The formula of simple interest is as below.
I = P*R*T÷100
Where I is interest.
P is Principle amount
R is rate of interest
T is time in years.
From your question, money becomes 10 times, it means, interest itself is 9th of P here and R is equal to T. So
9P = P*R*R/100
or 9P = P*R2/100
or 900P= P*R2
or 900 = R2
Hence R = 30%
The annual rate of interest = 30% (Option C)
Given :
Time period (T) = Rate of interest (R)
To find :
The annual rate of interest, R
Solution :
Simple interest = (Principal amount x Rate of interest x Time period)/100
= (P x R x T) / 100
It is said that the sum of the money becomes ten times itself at simple interest.
This means if P = x, then the amount A = 10x
Amount (A) = Principal amount (P) + Simple interest (SI)
⇒ 10x = x + SI
⇒ SI = 9x or 9P
Therefore, 9P = (P x R x T) /100
Given; R = T
⇒ 9P = (P x R²) / 100
⇒ 900 P = P x R²
⇒ R² = 900²
⇒ R = 30
The annual rate of interest = 30%
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