A sum of money invested at 5% p.a. simple interest amounts to Rs. 1,326 in 6years. In what time will it amount to Rs.1,530 ?
1) 8 years
2) 12 years
3) 10 years
4) 14 years
Answers
Answer:
Option (3)
Step-by-step explanation:
Given:-
A sum of money invested at 5% p.a. simple interest amounts to Rs. 1,326 in 6years.
To find :-
In what time will it amount to Rs.1,530 ?
Solution :-
Let the sum be Rs. X
P = Rs. X
Given Rate of interest = 5%
R = 5 %
Time = 6 years
T = 6 years
Amount = Rs. 1326
A = Rs. 1326
We know that
Simple Interest = PTR/100
And
Amount = Principle + Interest
=> 1326 = X + Interest
=> Interest = Rs. (1326-X)
Now, on Substituting these values in the above formula then
=> 1326-X = (X×6×5)/100
=> 1326-X = 30X/100
=> 1326-X = 3X/10
=>10(1326-X) = 3X
=> 10×1326 - 10×X = 3X
=> 13260 - 10X = 3X
=> 13260 = 3X+10X
=> 13260 = 13X
=> 13X = 13260
=> X = 13260/13
=> X = 1020
The Principle = Rs. 1020
And given that
Amount = Rs. 1530
Rate of interest = 5%
Now Let the required time be T years
So
Amount = Principle + Interest
=> 1530= 1020+Interest
=> 1530-1020 = Interest
=> 510 = Interest
Therefore, SI = Rs. 510
Now We have
P = Rs. 1020 , I = Rs. 510 , R = 5%
On Substituting these values in the formula
I = PTR/100
=> 510 =( 1020×T×5)/100
=> 510 = 5100 T/100
=> 510 = 51 T
=> 51T = 510
=> T = 510/51
=> T = 10
Therefore, T = 10 years
Answer:-
The required time for the given problem is
10 years
Used formulae:-
- Simple Interest = PTR/100
- Amount = Principle + Interest
- R = Rate of Interest
- T = Time