Question

A sum was put at simple interest at a certain rate for 2 years. Had it been put at 3% higher rate, it would have fetched rs.300 more. Find the sum

Answer 1

We have

 S.I = P x R x T /100

given I = 300, P =?, r = 3, t = 2 yrs

300 = P x 3 x 2 /100

6 P = 300 x 100 / 6

or P = rs 5000

OR

S.I for 2 yrs is rs 300

for 1 year it is 300/2 = rs 150

invested sum = 150 / 3 x 100 = Rs 5000

Answer 2

$\underline\mathfrak{Given:-}$

• A simple interest at a certain rate for 2 year, it been put at 3% heigher it would have fetching Rs. 300

$\underline\mathfrak{To \: \: Find:-}$

• Find the the sum ......?

$\underline\mathfrak{Solutions:-}$

• Let the sum be Rs. x.
• and the sum original rate be r%

Then,

Simple interest

$\: \: \: \: \: = \: \: \frac{x \: \times \: r \: \times \: {2}}{100}$

Now, rate is increase by 3%

New rate of interest = (r + 3)

Simple interest

$\: \: \: \: \: = \: \: \frac{x \: \times \: {(r \: + \: {3})} \: \times \: {2}}{100}$

According to the question:

$\: \: \: \: \: \leadsto \: \: {\frac{x \: \times \: {(r \: + \: {3})} \: \times \: {2}}{100}} \: - \: {\frac{x \: \times \: r \: \times \: {2}}{100}} \: \: = \: \: {300}$

$\: \: \: \: \: \leadsto \: \: {\frac{{(xr \: + \: {3x})} \: \times \: {2}}{100}} \: - \: {\frac{2xr}{100}} \: \: = \: \: {300}$

$\: \: \: \: \: \leadsto \: \: {\frac{{2xr} \: + \: {6x}}{100}} \: - \: {\frac{2xr}{100}} \: \: = \: \: {300}$

$\: \: \: \: \: \leadsto \: \: {\frac{\cancel{2xr} \: + \: {6x} \: - \: \cancel{2xr}}{100}} \: \: = \: \: {300}$

$\: \: \: \: \: \leadsto \: \: {\frac{6x}{100}} \: \: = \: \: {300}$

$\: \: \: \: \: \leadsto \: \: {x} \: \: = \: \: \frac{{300} \: \times \: {100}}{6}$

$\: \: \: \: \: \leadsto \: \: {x} \: \: = \: \: \cancel{\frac{30000}{6}}$

$\: \: \: \: \: \leadsto \: \: {x} \: \: = \: \: {5000}$

Hence, the sum is Rs. 5000.