Question

If the simple interest on rs. 2000 is less than the simple interest on rs. 3000 at 5% by rs. 50, find the time.

Answer 1

Let the Time Period be : T

We know that : Simple Interest is given by :

✿  $\bold{Interest = \frac{Principal\times Rate\;of\;Interest\times Time\;Period}{100}}$

Let us Find the Simple Interest for Rs.2000 :

Given : Principal = Rs. 2000 and Rate of Interest = 5%

$\bold{\implies Interest = (\frac{2000 \times 5 \times T}{100})}\\\\\bold{\implies Interest = 100T}$

Now, Let us Find the Simple Interest for Rs.3000 :

$\bold{\implies Interest = (\frac{3000 \times 5 \times T}{100})}\\\\\bold{\implies Interest = 150T}$

Given : The S.I on Rs. 2000 is Rs.50 less than S.I on Rs. 3000

⇒ Simple Interest on Rs. 3000 - Simple Interest on Rs. 2000 = 50

⇒ 150T - 100T = 50

⇒ 50T = 50

⇒ T = 1

So, The Time Period is 1 Year

Answer 2

Explanation:

Let the Time Period be : T

We know that : Simple Interest is given by :

✿ \bold{Interest = \frac{Principal\times Rate\;of\;Interest\times Time\;Period}{100}}Interest=

100

Principal×RateofInterest×TimePeriod

Let us Find the Simple Interest for Rs.2000 :

Given : Principal = Rs. 2000 and Rate of Interest = 5%

\begin{gathered}\bold{\implies Interest = (\frac{2000 \times 5 \times T}{100})}\\\\\bold{\implies Interest = 100T}\end{gathered}

⟹Interest=(

100

2000×5×T

)

⟹Interest=100T

Now, Let us Find the Simple Interest for Rs.3000 :

\begin{gathered}\bold{\implies Interest = (\frac{3000 \times 5 \times T}{100})}\\\\\bold{\implies Interest = 150T}\end{gathered}

⟹Interest=(

100

3000×5×T

)

⟹Interest=150T

Given : The S.I on Rs. 2000 is Rs.50 less than S.I on Rs. 3000

⇒ Simple Interest on Rs. 3000 - Simple Interest on Rs. 2000 = 50

⇒ 150T - 100T = 50

⇒ 50T = 50

⇒ T = 1

So, The Time Period is 1 Year