Question

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Answer 1

Answer:

the answer is above

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Answer 2

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