Question

itzAkshra ? 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 year. Determine the share of each in the principal.​

Answer 1

Step-by-step explanation:

441:400

Let the share of A= Rs. x.

Then Share of B= Rs. (84100−x)

∴x(1+

100

5

)

3

=(84100−x)(1+

100

5

)

5

Ratio of shares of A and B =

84100−x

x

=(1+

100

5

)

2

=(

20

21

)

2

=

400

441

Answer 2

Step-by-step explanation:

Given:

• Principal: Rs. 1682
• Rate: 5%

Solution:

Let Rahim's share = Rs. x

Then, Karim's share = Rs. (1682-x)

Rahim gets after 3 years = principal of Rahim

➛ $(1 + \frac{R}{100})^{T}$

➛ $x(1 + \frac{5}{100} ) ^{3}$

➛ $x(1 + \frac{1}{20} ) ^{3}$

➛ $x(\frac{20+1}{20} ) ^{3}$

➛ $x( \frac{21}{20} ) ^{3}$

Karim gets after 5 years = principal of Karim

➛ $(1 + \frac{R}{100})^{T}$

➛ $(1682 - x)(1 + \frac{5}{100} ) ^{5}$

➛ $(1682 - x)(1 + \frac{1}{20} ) ^{5}$

➛ $(1682 - x)(\frac{20+1}{20} ) ^{5}$

➛ $(1682 - x)(\frac{21}{20} ) ^{5}$

It's given that,

➛$x \times ( \frac{21}{20} ) ^{3} = (1682 - x)( \frac{21}{20} )^{5 }$

➛ $x =(1682 - x)( \frac{21}{20} ) ^{5} /( \frac{21}{20} ) ^{3}$

➛ $x =(1682 - x)( \frac{21}{20} ) ^{2}$

➛ (20)²x = (1682-x)(21)²

➛ 400x = (1682-x) 441

➛ 400x = 1682×441-411x

➛ 400x+441x = 1682× 441

➛ 841x = 1682×441

➛ x = $\frac{1682 \times 441}{841}$

➛ x = $\frac{741762}{841}$

➛ x = 882

∴ Rahim's share = Rs. 882

And, Karim's share = Rs. 800