# Rs.4,000 amounts to Rs.5,000 in 8 years; in what time will Rs.2,100 amount to Rs.2,800 at the same rate?

a) 10 years and 8 months

b) 8 years and 5 months

c) 11 years and 9 months

d) 13 years and 5 months

Last updated date: 31st Mar 2023

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Answer

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Hint: To solve the question, we have to apply the appropriate formulae of simple interest. To calculate the rate of interest, use the data of the first case. The obtained value of rate of interest when applied for the data of the second case we can calculate the time period.

Complete step-by-step answer:

Given,

Amount = Rs. 5000

Principal amount = Rs.4000

Time period = 8 years

We know that the formula for simple interest is given by A = SI + P

Where A, SI, P represent the amount, simple interest and principal amount respectively.

By substituting the given values in the above formula, we get

$\Rightarrow$ 5000 = SI + 4000

$\Rightarrow$ SI = 5000 – 4000 = Rs. 1000

We know that the formula for simple interest is given by \[\dfrac{PRT}{100}\]

where R, T represent rate of interest and time period respectively.

By substituting the given and obtained values in the above formula, we get

$\Rightarrow$ \[SI=\dfrac{4000\times R\times 8}{100}\]

$\Rightarrow$ \[1000=\left( 40\times 8 \right)R\]

$\Rightarrow$ \[1000=320R\]

$\Rightarrow$ \[R=\dfrac{1000}{320}=3.125%\]

Now to calculate the value of Simple interest for Amount = Rs. 2800 and principal amount = Rs.2100 at the same rate, substitute these values in the above formula.

Thus, we get

$\Rightarrow$ 2800 = SI + 2100

$\Rightarrow$ SI = 2800 – 2100 = Rs. 700

By substituting the given and obtained values in the above formula, we get

$\Rightarrow$ \[SI=\dfrac{2100\times 3.125\times T}{100}\]

$\Rightarrow$ \[700=\left( 21\times 3.125 \right)T\]

$\Rightarrow$ \[700=65.625T\]

$\Rightarrow$ \[T=\dfrac{700}{65.625}=10.6667\]years

We know that \[\dfrac{8}{12}=0.6667\]

10.6667 years = 10 years 8 months

Thus, The amount Rs.2,100 increments to Rs.2,800 at the same rate in 10 years 8 months.

Hence, option (a) is the right choice.

Note: The possibility of mistake can be not using appropriate formula, though the question doesn’t exclusively mention simple interest, it has to be understood since the required parameters to calculate simple interest are given.

Complete step-by-step answer:

Given,

Amount = Rs. 5000

Principal amount = Rs.4000

Time period = 8 years

We know that the formula for simple interest is given by A = SI + P

Where A, SI, P represent the amount, simple interest and principal amount respectively.

By substituting the given values in the above formula, we get

$\Rightarrow$ 5000 = SI + 4000

$\Rightarrow$ SI = 5000 – 4000 = Rs. 1000

We know that the formula for simple interest is given by \[\dfrac{PRT}{100}\]

where R, T represent rate of interest and time period respectively.

By substituting the given and obtained values in the above formula, we get

$\Rightarrow$ \[SI=\dfrac{4000\times R\times 8}{100}\]

$\Rightarrow$ \[1000=\left( 40\times 8 \right)R\]

$\Rightarrow$ \[1000=320R\]

$\Rightarrow$ \[R=\dfrac{1000}{320}=3.125%\]

Now to calculate the value of Simple interest for Amount = Rs. 2800 and principal amount = Rs.2100 at the same rate, substitute these values in the above formula.

Thus, we get

$\Rightarrow$ 2800 = SI + 2100

$\Rightarrow$ SI = 2800 – 2100 = Rs. 700

By substituting the given and obtained values in the above formula, we get

$\Rightarrow$ \[SI=\dfrac{2100\times 3.125\times T}{100}\]

$\Rightarrow$ \[700=\left( 21\times 3.125 \right)T\]

$\Rightarrow$ \[700=65.625T\]

$\Rightarrow$ \[T=\dfrac{700}{65.625}=10.6667\]years

We know that \[\dfrac{8}{12}=0.6667\]

10.6667 years = 10 years 8 months

Thus, The amount Rs.2,100 increments to Rs.2,800 at the same rate in 10 years 8 months.

Hence, option (a) is the right choice.

Note: The possibility of mistake can be not using appropriate formula, though the question doesn’t exclusively mention simple interest, it has to be understood since the required parameters to calculate simple interest are given.

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