Question

Amar and Anand borrowed ₹2000 and ₹3000 respectively at the same rate of simple interest for 3 years . If anand paid ₹ 150 more interest than Amar , find the rate of interest per annum​

Answer 1

Answer: 5%

Given:

Case 1: Amar

• P = Rs. 2000
• R = x %
• T = 3 years
• SI = Some variable 'y'

Case 2: Anand

• P = Rs. 3000
• R = x %
• T = 3 years
• SI = y + 150

To find:

• Rate of interest per annum (x)

Solution:

Let's first calculate the SI for Amar.

$\boxed{SI = \dfrac{P \times R \times T}{100}}$

Therefore,

$\implies \text{SI for Amar} = \dfrac{ 2000 \times x \times 3}{100}\\\\\\\implies \boxed{\text{SI for Amar} = 60x}$

Now, let's calculate the SI for Anand.

Therefore we get:

$\implies \text{SI for Anand} = \dfrac{ 3000 \times x \times 3}{100}\\\\\\\implies \boxed{\text{SI for Anand} = 90x}$

From the given information, we know that:

→ SI of Anand = SI of Amar + 150

Substituting respective SI's we get:

→ 90x = 60x + 150

→ 90x - 60x = 150

→ 30x = 150

→ x = 150/30

→ x = 5%

Hence the rate of interest per annum is 5%.

Answer 2

Answer:

According to the question,

\( \Large \frac{3000 \times 5 \times R}{100 \times 2}-\frac{2000 \times 5 \times R}{100 \times 2} =125\)

\( \Large \frac{1}{200}\left[ 15000R-10000R \right]=125 \)

\( \Large \frac{5000R}{200}=125 \)

R= 5 \%