Question

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

Answer 1

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

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

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

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

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

$\sf{\implies Amount\:_{(after\:3\: years)}=?}$

$\sf{\implies Principal=?}$

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

To calculate the amount after 3 years at first we have to assume the sum of money be P then calculate amount after 3 years. By applying formula we can easily find the amount.

$\sf\large\underline{Formula\:used:-}$

$\tt{\implies SI=Amount-Principal}$

$\tt{\implies SI=4491-P}$

• Now calculate principal here:]
• Here T=24+3/12=27/12=9/4

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

$\tt{\implies P=\dfrac{(4491-P)*100*4}{9*11}}$

$\tt{\implies P=\dfrac{(4491-P)*100*4}{99}}$

$\tt{\implies P=\dfrac{(4491-P)*400}{99}}$

$\tt{\implies P=\dfrac{898200-400P}{99}}$

$\tt{\implies 99P=1796400-400P}$

$\tt{\implies 99P+400P=1796400}$

$\tt{\implies 499P=1796400}$

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

• Now calculate SI for 3 years:]

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

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

$\tt{\implies SI=\dfrac{3600*33}{100}}$

$\tt{\implies SI=36*33}$

$\tt{\implies SI=1188}$

• Now calculate amount for 3 years:]

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

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

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

$\sf\large{Hence,}$

$\sf{\implies Amount\:_{(after\:3\: years)}=Rs.4788}$

Answer 2

Answer:

As we know that SI = P x R x T /100 (Where P = Principal Amount, R = Rate of Interest and T = Time).

Let us assume that the principal amount be Rs. X.

Then the SI will be Rs (4491 - X)

Rate of interest = 11% and Time = 2 yrs 3 months = 2 yrs 3/12 = 2.25 yrs.

So (4491 - X) = X * 11 * 2.25/100

(4491 - X) = 24.75X/100

449100 - 100X = 24.75X

-100X - 24.75X = - 449100

-124.75X = -449100

X = - 449100/- 124.75 = 3600.

So the Principal amount is equal to Rs. 3600.

Now the second part of the problem:

SI = PxRxT/100 (Where P = Rs 3600, R = 11% and T = 3yrs)

SI = 3600 x 11 x 3/100 =Rs. 1188.

So the amount will be Rs. (3600 + 1188) = Rs. 4788.

Ans: Rs. 4788.

Step-by-step explanation: