Certain amount of money was lent at 8% per annum simple intrest. After 1 year, rs7200 was repaid and the remaining amount was repaid at 5% simple intrest. Of the 2nd years intrest is 2/5 of the 1st year intrest . Find the original amount which was lent.
Answers
Step-by-step explanation:
Given :-
Certain amount of money was lent at 8% per annum simple intrest. After 1 year, rs7200 was repaid and the remaining amount was repaid at 5% simple intrest. Of the 2nd years intrest is 2/5 of the 1st year intrest .
To find :-
Find the original amount which was lent ?
Solution :-
Let the amount was lent be Rs. X
The Principle (P) = Rs. X
Rate of interest (R) = 8%
Time (T) = 1 Year
We know that
Simple Interest = PTR/100
Simple Interest for 1 year = (X×1×8)/100
=> SI 1 = 8X/100
=> SI 1 = Rs. 2X/25
We know that
Amount = Principle + Interest
=> Amount after 1 year = X+(2X/25)
=> (25X+2X)/25
=> 27X/25
Amount to be paid after 1 year
= Rs. 27X/25
Given that
Amount was paid after 1 year = Rs. 7200
Remaining amount = (27X/25)-7200
=> Rs. (27X-180000)/25
Now,
New principle = Rs. (27X-180000)/25
Rate of interest for the remaining amount = 5%
Time (T) = 1 year
Simple Interest for second year
= PTR/100
=> SI 2= [(27X-180000)×1×5]/(25 ×100)
=> SI 2 = (27X-180000)×5/2500
=> SI 2 = Rs. (27X-180000)/500
Given that
2nd years intrest is 2/5 of the 1st year intrest .
=> SI 2 = (2/5)× SI 1
=> (27X-180000)/500 = (2/5)×(2X/25)
=> (27X-180000)/500 = (2×2X)/(5×25)
=> (27X-180000)/500 = 4X/125
On applying cross multiplication then
=> (27X-180000)×125 = 4X×500
=> (27X-180000) ×125 = 2000X
=> (27X-180000) = 2000X/125
=> (27X-180000) = 16X
=> 27X -16X = 180000
=> 11X = 180000
=>X = 180000/11
=> X = 16363. 6363...
=> X = Rs. 16363.64
Therefore, X = Rs. 16363.64
Answer:-
The Original amount was lent for the given problem is Rs. 16363.64
Used formulae:-
→ Simple Interest = PTR/100
→ Amount = Principle + Interest
Check:-
Principle = Rs. 16363 (round off it two nearest ten thousands)
Rate of interest = 8%
Time = 1 year
SI = (16363×1×8)/100
=> SI = 130904/100
=> SI = 1309.04
Amount = 16363+1309
=> A = 17667
Amount was paid = Rs. 7200
Remaining = 17667-7200
=> 10467
Simple Interest for the second year
=> (10467×1×5)/100
=> 52337/100
=> 523.37
=> Rs. 523
SI for 2 nd year = Rs. 523 ------(1)
Now,
2/5th of SI for the first year
=> (2/5)×1309
=> 2618./5
=> 523.6
=> 523-----(2)
From (1)&(2)
Verified the given relations in the given problem.