Question

A sum of money put at 11% per annum amounts to Rs 4491 in 2 years 3 months. What will it amount to in 3 years at the same rate?

Answer 1

$\sf\large\underline{Let:-}$

$\sf{\implies The\:sum\:of\: money=X}$

$\sf\large\underline{Given:-}$

$\sf{\implies Amount=Rs.4491}$

$\sf{\implies Time=2\: years\:3\: months}$

$\sf{\implies Interest=11\%}$

$\sf\large\underline{To\:Find:-}$

$\sf{\implies Amount\:_{(at\:the\:end\:of\:3\: years)}=?}$

$\sf\large\underline{Solution:-}$

To calculate amount at the end of 3 years , at first we have to find out simple interest then calculate principal or sum of money. At last we have to find amount for 3 years at same interest which is given in the question. Before calculate simple interest at first we have to calculate time as per the annual interest per year ,so 2years 3months which is equal to 2 whole 3/12 or 27/12=> 9/4 years:

$\tt{\implies SI=\dfrac{P\times\:T\times\:R}{100}}$

$\tt{\implies SI=\dfrac{x\times\:9\times\:11}{100\times\:4}}$

$\tt{\implies SI=\dfrac{99x}{400}}$

• Now calculate calculate P here:]

$\sf{\implies Amount=P+SI}$

$\tt{\implies 4491=x+\dfrac{99x}{400}}$

$\tt{\implies 4491=\dfrac{400x+99x}{400}}$

$\tt{\implies 4491=\dfrac{499x}{400}}$

$\tt{\implies 4491\times\:400=499x}$

$\tt{\implies 9\times\:400=x}$

$\tt{\implies x=Rs.3600}$

• Now calculate amount for 3 years:]

$\tt{\implies SI=\dfrac{3600\times\:3\times\:11}{100}}$

$\tt{\implies SI=36\times\:3\times\:11}$

$\tt{\implies SI=Rs.1188}$

$\sf{\implies Amount\:_{(for\:3\: years)}=P+SI}$

$\sf{\implies Amount=3600+1188}$

$\sf{\implies Amount=Rs.4788}$

$\sf\large{Hence,}$

$\sf{\implies Amount\:_{(at\:the\:end\:of\:3\: years)}=Rs.4788}$

Answer 2

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Question

A sum of money put at 11% per annum amounts to Rs 4491 in 2 years 3 months. What will it amount to in 3 years at the same rate?

$\large{\underline{\underline{\sf{\purple{ Required\: Ansωєr}}}}}$

Given:-

$\tt{\implies}$ Amount = Rs.4491

$\tt{\implies}$Time = 2 years 3 months

$\tt{\implies}$ Interest = 11%

To Find:-

Amount (at the end of 3 years) = ?

Solution:-

Let Principle money = x

We know simple interest $\tt{\implies \dfrac{PRT}{100}}$

Here,

• Interest = ( 4491 - x ) rs
• Rate ( R ) = 11%
• time ( T )= 2 +$\tt{\implies \dfrac{3}{12}}$

• = 2.25 years.

So,

• 4491 - $\tt{\implies \dfrac{X × 11 × 2.25}{100}}$

• 449100 - 100x = 24.75x

• 124.75x = 449100

• x = 3600

So he has sum of money in starting is = 3600 Rs.

• Now he gets after three year

• here P = 3600 , R = 11% And T = 3years

• Interest $\tt{\implies \dfrac{3600×11×3}{100}}$

Interest = 1188 Rs

• So total amount will be = 3600 + 1188 = 4788 Rs

${\underline {\underline {\boxed {\rm {\red { Ans\:4788\:Rs }}}}}}$

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