Question

Ravi invests some money at 12% simple interest and some other money at 10% simple interest and receives ₹ 2600 as yearly interest. If he had interchanged the amounts, he would have received ₹ 80 more as yearly interest. How much did he invest at different rates?

Answer 1

Given:

• Ravi invests two amounts one at 12% simple interest and the other at 10% simple interest.
• The total yearly interest from both investments is ₹ 2600.
• If the amounts invested at 12% and 10% are interchanged, Ravi would receive ₹ 80 more as yearly interest.

Step-wise calculation:

1. Let the amount invested at 12% be ₹ x.

2. Then, the amount invested at 10% = ₹ (y).

3. The yearly interest from these investments is:

`12/100 xx x + 10/100 xx y = 2600`

or 0.12x + 0.10y = 2600   ...(Equation 1)

4. If the amounts are interchanged, the interest becomes:

`12/100 xx y + 10/100 xx x = 2600 + 80`

`12/100 xx y + 10/100 xx x = 2680`

or 0.12y + 0.10x = 2680   ...(Equation 2)

5. Multiply Equation 1 by 10 and Equation 2 by 10 to avoid decimals: 

1.2x + 1.0y = 26000   ...(1) 

1.0x + 1.2y = 26800   ...(2)

6. Multiply Equation (2) by 1.2: 

1.2x + 1.44y = 32160

7. Subtract Equation (1) from the above: 

(1.2x + 1.44y) – (1.2x + 1.0y) = 32160 – 26000 

0.44y = 6160

`y = 6160/0.44`

y = 14000

8. Substitute (y = 14000) in Equation (1): 

1.2x + 1.0 × 14000 = 26000 

1.2x + 14000 = 26000 

1.2x = 12000 

`x = 12000/1.2`

x = 10000

Amount invested at 12% = ₹ 10,000.

Amount invested at 10% = ₹ 14,000.