If the compound interest on a certain sum for two years at 10% p.a. is Rs 3200 and the simple interest on other Sum at the same rate for two years will be 12000. What is the sum of the principal?
Answers
Answer:
hope it helps you siso...
Explanation:
Given :-
the compound interest on a certain sum for two years at 10% p.a. is Rs 3200 and the simple interest on other Sum at the same rate for two years will be 12000.
To find :-
What is the sum of the principal?
Solution :-
Let the principle be Rs. X
Rate of interest (R) = 10%
Time =2 years
Compound interest = Rs. 3200
We know that
A = P[1+(R/100)]^n
On Substituting these values in the above formula
=> A = X[1+(10/100)]²
=> A = X[1+(1/10)]²
=> A = X[(10+1)/10]²
=> A = X(11/10)²
=> A = X(121/100)
=> A = 121X/100
Amount = Rs. 121X/100
We know that
A = P + I
=> P = A - I
=> X = (121X/100)-3200
=> X = (121X-320000)/100
=> X×100 = 121X-320000
=> 100X = 121X-320000
=> 100X-121X = -320000
=> -21X = -320000
=> 21 X = 320000
=> X = 320000/21
=> X = 15238.095
=> X = Rs. 15238
and
Rate of interest = 10%
Simple Interest = Rs. 12000
Time = 2 years
Let the Principle be Rs. X
We know that
Simple Interest = PTR/100
On Substituting these values in the above formula then
=> 12000 = (X×2×10)/100
=> 12000 = 20X/100
=> 12000 = X/5
=> X = 12000×5
=> X = Rs. 60000
The principle in the first condition = Rs. 15238
The principle in the second condition =
Rs. 60000
The sum of the principles
= 15238+60000
= Rs. 75238
Answer :-
The sum of the principles for the given problem is Rs. 75238
Used formulae:-
- A = P[1+(R/100)]^n
- A = P + I
- Simple Interest = PTR/100
Where,
- I = Interest
- A = Amount
- P = Principle
- T = Time
- R = Rate of Interest
- n = Number of times the compound interest is calculated.