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Rs. 260200 is divided between Ram and Shyam so that the amount that Ram receives in 3 years is the same as that Shyam receives in 6 years. If the interest is compounded annually at the rate of 4% per annum then Ram's share is = ?

1Rs. 12500
2Rs. 137745.02
3Rs. 15200
4Rs. 108200

Answer:- 1

Explanation:-

Solution:

Let Ram get Rs. x and
Shyam get Rs. (260200 - x)
Then Amount get by Ram after 3 years

= x \times {(1 + \frac{4}{100})}^{3}

${\text{ = }}x \times {\left( {1 + \frac{4}{{100}}} \right)^3}$
and Amount get by Shyam after 6 years

= (260200 - x) \times {(1 + \frac{4}{100})}^{6}

$= \left( {260200 - x} \right) \times {\left( {1 + \frac{4}{{100}}} \right)^6}$

\begin{aligned} But both get equal amount \\ ∴ x \times {(1 + \frac{4}{100})}^{3} = (260200 - x) \times {(1 + \frac{4}{100})}^{6} \\ \Rightarrow \frac{x}{2600200 - x} = \frac{17576}{15625} \\ \Rightarrow 15625 x = 4573275200 - 17576 x \\ \Rightarrow 33201 x = 4573275200 \\ \Rightarrow x = 137745.022 \end{aligned}

$\eqalign{ & {\text{But both get equal amount }} \cr & \therefore x \times {\left( {1 + \frac{4}{{100}}} \right)^3} = \left( {260200 - x} \right) \times {\left( {1 + \frac{4}{{100}}} \right)^6} \cr & \Rightarrow \frac{x}{{2600200 - x}} = \frac{{17576}}{{15625}} \cr & \Rightarrow 15625x = 4573275200 - 17576x \cr & \Rightarrow 33201x = 4573275200 \cr & \Rightarrow x = 137745.022 \cr}$

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and Amount get by Shyam after 6 years

= (260200 - x) \times {(1 + \frac{4}{100})}^{6}

$= \left( {260200 - x} \right) \times {\left( {1 + \frac{4}{{100}}} \right)^6}$

\begin{aligned} But both get equal amount \\ ∴ x \times {(1 + \frac{4}{100})}^{3} = (260200 - x) \times {(1 + \frac{4}{100})}^{6} \\ \Rightarrow \frac{x}{2600200 - x} = \frac{17576}{15625} \\ \Rightarrow 15625 x = 4573275200 - 17576 x \\ \Rightarrow 33201 x = 4573275200 \\ \Rightarrow x = 137745.022 \end{aligned}

$\eqalign{ & {\text{But both get equal amount }} \cr & \therefore x \times {\left( {1 + \frac{4}{{100}}} \right)^3} = \left( {260200 - x} \right) \times {\left( {1 + \frac{4}{{100}}} \right)^6} \cr & \Rightarrow \frac{x}{{2600200 - x}} = \frac{{17576}}{{15625}} \cr & \Rightarrow 15625x = 4573275200 - 17576x \cr & \Rightarrow 33201x = 4573275200 \cr & \Rightarrow x = 137745.022 \cr}$ ", "dateCreated": "7/24/2019 10:09:12 AM", "author": { "@type": "Person", "name": "Nitin Sir" } }, "suggestedAnswer": { "@type": "Answer", "text": "

Solution:

Let Ram get Rs. x and
Shyam get Rs. (260200 - x)
Then Amount get by Ram after 3 years

= x \times {(1 + \frac{4}{100})}^{3}

${\text{ = }}x \times {\left( {1 + \frac{4}{{100}}} \right)^3}$
and Amount get by Shyam after 6 years

= (260200 - x) \times {(1 + \frac{4}{100})}^{6}

$= \left( {260200 - x} \right) \times {\left( {1 + \frac{4}{{100}}} \right)^6}$

\begin{aligned} But both get equal amount \\ ∴ x \times {(1 + \frac{4}{100})}^{3} = (260200 - x) \times {(1 + \frac{4}{100})}^{6} \\ \Rightarrow \frac{x}{2600200 - x} = \frac{17576}{15625} \\ \Rightarrow 15625 x = 4573275200 - 17576 x \\ \Rightarrow 33201 x = 4573275200 \\ \Rightarrow x = 137745.022 \end{aligned}

$\eqalign{ & {\text{But both get equal amount }} \cr & \therefore x \times {\left( {1 + \frac{4}{{100}}} \right)^3} = \left( {260200 - x} \right) \times {\left( {1 + \frac{4}{{100}}} \right)^6} \cr & \Rightarrow \frac{x}{{2600200 - x}} = \frac{{17576}}{{15625}} \cr & \Rightarrow 15625x = 4573275200 - 17576x \cr & \Rightarrow 33201x = 4573275200 \cr & \Rightarrow x = 137745.022 \cr}$ ", "dateCreated": "7/24/2019 10:09:12 AM" } }

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