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Answers
Step-by-step explanation:
Given :-
Two partners Rahim and Karim together lend 1,682 at 5% p.a. compounded annually.The amount Rahim gets at the end of 3 years is same as Karim gets at the end of 5 years.
To find :-
Determine the share of each in the principle ?
Solution :-
Given that
The amount is lent by Rahim and Karim together = Rs. 1682
Let the amount lent by Rahim be Rs. X
The amount lent by Karim be Rs. (1682-X)
Rate of Interest = 5%
Amount after 3 years compondly for Rahim
We know that
Amount = P[1+(R/100)]^n
=> A = X[1+(5/100)]³
=> A = X[1+(1/20)]³
=> A = X[(20+1)/20]³
=> A = X(21/20)³
Rahim will get Rs. X(21/20)³ after 3 years
and
The amount after 5 years for Karim
Amount = P[1+(R/100)]^n
=> A = (1682-X)[1+(5/100)]⁵
=> A =(1682- X)[1+(1/20)]⁵
=> A = (1682-X)[(20+1)/20]⁵
=> A = (1682-X)(21/20)⁵
Karim will get Rs. (1682-X)(21/20)⁵ after 5 years
According to the given problem
They are same
(1682-X)(21/20)⁵ = X(21/20)³
=> (21/20)⁵/(21/20)³ = X/(1682-X)
=> (21/20)⁵-³ = X/(1682-X)
=> (21/20)² = X/(1682-X)
=> 441/400 = X/(1682-X)
On applying cross multiplication then
=> (1682-X)441 = 400X
=> 1682×441 - 441X = 400X
=> 741762 -441X = 400X
=> 741762 = 400X+441X
=> 741762 = 841X
=> X = 741762/841
=> X =Rs. 882
The amount lent by Rahim = Rs. 882
The amount lent by Karim = 1682-882 = Rs. 800
Answer:-
The principle of Rahim = Rs. 882
The principle of Karim = Rs. 800
Used formulae:-
Amount = P[1+(R/100)]^n
P = Principle
R = Rate of Interest
n = Number of times the interest is calculated per annum compoundly.
A = amount