Question

Ram and Shyam together lent Rs. 3364 at 5% compound interest, compounded
annuslly. The amount Ram gets at the end of three years is the same as
Shyam gets at the end of five years. The share of Ram in principal amount is
​

Answer 1

If Ram and Shyam together lent Rs. 3364 at 5% compound interest, compounded  annually, then the share of Ram in principal amount is Rs. 1764.

Step-by-step explanation:

Required Formula:

Amount, A = P [1+R/100]ⁿ

The principal amount lent by Ram and Shyam together = Rs. 3364  

So, let the share of Ram in principal amount be Rs. “P”, then the share of Shyam in principal amount would be Rs. “[3364 - P]” .

Rate of interest for both, R = 5% p.a.

Time period for Ram = 3 year

Time period for Shyam = 5 year

Now, according to the question and based on the above formula we can write the eq. as,

P * [1 + $\frac{5}{100}$]³ = [3364 - P] * [1 + $\frac{5}{100}$]⁵

cancelling the similar terms

⇒ P = [3364 - P] * [1 + $\frac{5}{100}$]²

⇒ P = [3364 - P] * [1 + $\frac{1}{20}$]²

⇒ P = [3364 - P] * [$\frac{21}{20}$]²

⇒ P = [3364 - P] * [$\frac{441}{400}$]

⇒ 400P = 1483524 – 441P

⇒ 400P + 441P = 1483524

⇒ 841P = 1483524

⇒ P = $\frac{1483524}{841}$

⇒ P = Rs. 1764

Thus, the share of Ram in principal amount is Rs. 1764.

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Answer 2

Given :  Ram and Shyam together lent Rs. 3364 at 5% compound interest, compounded annuslly.

The amount Ram gets at the end of three years is the same as Shyam gets at the end of five years.

To Find : The share of Ram in principal amount  

Solution:

Ram Amount  =  P   Rs

Shyam Amount = 3364 - P  Rs

A = P ( 1+ R/100)ⁿ

R = 5 %

The amount Ram gets at the end of three years

= P ( 1 + 5/100)³

= P ( 1.05)³

The amount Shyam gets at the end of 5 years

=  (3364 - P) ( 1 + 5/100)⁵

= (3364 - P) ( 1.05)⁵

(3364 - P) ( 1.05)⁵ = P ( 1.05)³

=> (3364 - P) ( 1.05)² = P  

=> (3364 - P) ( 1.1025)  = P  

=> 3,708.81 - 1.1025P = P

=> 2.1025P =  3,708.81

=> P = 1,764

The share of Ram in principal amount is  1,764 Rs

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