Raj invested a certain sum of money in a simple interest bond whose value grew to Rs. 400 at
the end of 3 years and to Rs. 500 at the end of another 5 years. What was the rate of interest in
which he invested his sum?
4.55%
5.88%
6.20%
8%
Answers
Step-by-step explanation:
Let principle be P and rate of interest is r.
Then, P×r×8100+P=300 ... (i)
and P×r×8100+P=400 ... (ii)
Subtracting Eq. (i) from Eq. (ii), we get
P×r×5100=100
Therefore, P×r=2000
From Eq. (i).
200×3100+P=300 =>P = Rs.240
Therefore, 24×r=2000
=> r = 5.88
Answer:
The rate at which the sum was invested is 5.88%
Step-by-step explanation:
Consider the :
- Rate as R
- Principal as P
Formula here used is : SI = PRT/100
Amount at the end of 3 years = Rs. 400
Amount at the end of 8 years (3 + 5) = Rs. 500
Interest got on the money in the 5 years =
⇒ 500 - 400
⇒ Rs. 100
The interest received each year =
⇒ 100/5
⇒ Rs. 20
Interest received on 3 years =
⇒ 3 × 20
⇒ Rs. 60
___________________________
Principal invested =
As, Amount = Principal + SI
⇒ Principal = Amount in 3 years - Interest in 3 years
⇒ Principal = 400 - 60
⇒ Principal = Rs. 340
___________________________
Rate of interest by which the sum was invested :
We have -
- Principal = Rs. 340
- Rate = R
- Time = 1 year
- SI = Rs. 20
⇒ 20 = (340 × R × 1)/100
⇒ 200 = 34R
⇒ R = 200/34
⇒ R = 5.88 %
Therefore, the rate at which the sum was invested is 5.88%