Q. Divide Rs. 1200 into two parts such that the simple interest on the first part for 2 yrs at 6% per annum is equal to the simle interest on the second part for 3 yrs at 8% per annum.
Answers
Answer:
Rs. 800 and Rs. 400
Step-by-step explanation:
Given :-
On Dividing Rs. 1200 into two parts such that the simple interest on the first part for 2 yrs at 6% per annum is equal to the simle interest on the second part for 3 yrs at 8% per annum.
To find :-
Find the two parts ?
Solution :-
Given that :
The amount is divided into two parts = Rs. 1200
Let The first part be Rs. X
Then the second part = Rs. (1200-X)
Now ,
We have , Principle = Rs. X
Rate of Interest on first part = 6%
Time = 2 years
We know that
Simple Interest = PTR/100
=> SI = (X×2×6)/100
=> SI = 12X/100
=> SI = 3X/25
Simple Interest = Rs. 3X/25 ----------(1)
and
The second part = Rs. (1200-X)
Principle = Rs. (1200-X)
Rate of Interest on first part = 8%
Time = 3 years
We know that
Simple Interest = PTR/100
=> SI = ((1200-X)×3×8)/100
=> SI = (1200-X)×24/100
=> SI = (1200-X)×6/25
=> SI = (7200-6X)/25
Simple Interest = Rs.(7200-6X)/25--------(2)
According to the given problem
The simple interest on the first part for 2 yrs at 6% per annum is equal to the simle interest on the second part for 3 yrs at 8% per annum.
=> (1) = (2)
=> 3X/25 = (7200-6X) /25
On cancelling 25 both sides
=> 3X = 7200-6X
=> 3X + 6X = 7200
=> 9X = 7200
=> X = 7200/9
=> X = 800
So, The first part = Rs. 800
The second part = 1200-800 = Rs. 400
Answer:-
The required two parts for the given problem are Rs. 800 and Rs. 400
Used formulae:-
- Simple Interest = PTR/100
- P = Principle
- T = Time
- R = Rate of Interest