A sum of money, lent out at simple interest, doubles itself in 8 years. Find :
(i) the rate of interest
(ii) in how many years will the sum become triple (three times) of itself at the same rate percent?
Solution
Let P = Rs.100, A = Rs.200
I = Rs.200 − Rs.100 = Rs.100, T = 8 years
R =`(100xx"I")/("P"xx"T")=(100xx100)/(100xx8)`
`=100/8=25/2%`
Now again P = Rs.100
A = Rs.300
I = Rs.300 − Rs.100 = Rs.200
R = `25/2%`
T =`(100xx"I")/("P"xx"R")=(100xx200)/(100xx25/2)=(100xx200xx2)/(100xx25)`
= 16 Years
So the given sum of money will become triple in 16 years.
Concept: Concept of Principal, Interest, Amount, and Simple Interest
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Free
SSC GD Previous Paper 2 (Held On: 13 Feb 2019 Shift 1)_Hindi
100 Questions 100 Marks 90 Mins
Given:
Amount = 3/2 of the sum
Time = 3 years
Formula used:
Simple interest = (P × R × T)/100
Amount = Principal + Interest
Calculation:
Let the sum of money be P
Amount after 3 years will be 3/2P
Now, by using the formula
3/2P – P = (PR × 3)/100
⇒ R = 50/3 = 16\(\frac{2}{3}\)%
∴ The rate of interest is 16\(\frac{2}{3}\)%.
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A sum becomes three times of itself in 10 years at the rate of simple interest. What is the rate of interest per annum?
- 25%
- 20%
- 15%
- 30%
Answer (Detailed Solution Below)
Option 2 : 20%
Free
CT : GK (Ancient History)
10 Questions 10 Marks 6 Mins
Given:
A sum becomes three times of itself in 10 years at the rate of simple interest
Amount(A) = 3Principal(P)
Time(T) = 10
Rate(R)
Formula Used:
Amount = Principal + Simple Interest(S.I)
S.I = (P × R × T)/100
Calculation:
Here A = 3P
⇒ 3P = P + ((P × 10 × R)/100)
⇒ 3P = P (1 + (10 × R)/100)
⇒ 300 = 100 + 10R
⇒ 10R = 200
⇒ R = 20%
∴ The rate of interest per annum is 20%.
Formula used:
S.I = A - P
S.I = (P × R × T)/100
Calculation:
Here A = 3P
⇒ S.I = 3P - P
⇒ S.I = 2P
⇒ 2P = P × R × 10/100
⇒ R = 2 × 10 = 20%
∴ The rate of interest per annum is 20%.
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