Question
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 = ?
Answer: Option B
Let Ram get Rs. x and
Shyam get Rs. (260200 - x)
Then Amount get by Ram after 3 years
$${\text{ = }}x \times {\left( {1 + \frac{4}{{100}}} \right)^3}$$
and Amount get by Shyam after 6 years
$$ = \left( {260200 - x} \right) \times {\left( {1 + \frac{4}{{100}}} \right)^6}$$
But both get equal amount
$$\therefore x \times {\left( {1 + \frac{4}{{100}}} \right)^3} = \left( {260200 - x} \right) \times $$ $${\left( {1 + \frac{4}{{100}}} \right)^6}$$
$$\eqalign{
& \Rightarrow \frac{x}{{2600200 - x}} = \frac{{17576}}{{15625}} \cr
& \Rightarrow 15625x = 4573275200 - 17576x \cr
& \Rightarrow 33201x = 4573275200 \cr
& \Rightarrow x = 137745.022 \cr} $$
So, Ram will get Rs. 137745.022
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Let Ram get Rs. x and
Shyam get Rs. (260200 - x)
Then Amount get by Ram after 3 years
$${\text{ = }}x \times {\left( {1 + \frac{4}{{100}}} \right)^3}$$
and Amount get by Shyam after 6 years
$$ = \left( {260200 - x} \right) \times {\left( {1 + \frac{4}{{100}}} \right)^6}$$
But both get equal amount
$$\therefore x \times {\left( {1 + \frac{4}{{100}}} \right)^3} = \left( {260200 - x} \right) \times $$ $${\left( {1 + \frac{4}{{100}}} \right)^6}$$
$$\eqalign{
& \Rightarrow \frac{x}{{2600200 - x}} = \frac{{17576}}{{15625}} \cr
& \Rightarrow 15625x = 4573275200 - 17576x \cr
& \Rightarrow 33201x = 4573275200 \cr
& \Rightarrow x = 137745.022 \cr} $$
So, Ram will get Rs. 137745.022
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