Question

3. Ravi gave 1200 on loan. Some amount he gave
at 4% per annum simple interest and remaining
at 5% per annum simple interest. After two years
he
110 as interest. What are the amounts
given at 4% and 5% per annum simple interest
respectively?
​

Answer 1

Answer:

The answer is 10 years.

This is a simple question based on the application of the simple interest formula.

We know that simple interest

SI = PTR/100

where SI = Simple Interest

P = Principal

T = Time

R = Rate of Interest

We do not know either the time or the principal amount here. Hence, we will be using simultaneous linear equations.

We have Amount = Principal + Simple Interest

Thus, Simple Interest = Amount - Principal

SI = A - P

From the first statement, we can write the following equation:

1120 - P = (P*T*4)/100

From the second statement, we can write:

1200 - P = (P*T*5)/100

Let us divide these two equations. Then, we get

\frac{1120-P}{1200-P}  =  \frac{4}{5}  

By cross multiplication, we get

4 ( 1200 - P ) = 5 ( 1120 - P )

4800 - 4 P = 5600 - 5 P

P = 5600 - 4800

P = 800

Thus, the principal amount is 800.

Let us use this in the first equation. It will become

1120 - 800 = (800*T*4)/100

320 = 8*4*T

320 = 32 T

T = 320/32

T = 10

Thus, the time period is 10 years. This value can be applied in the second equation also to verify the answer obtained.

This is probably one of the several methods which can be used to derive this answer. However, the end result will be the same. If you find any other method to be easier and quicker, you can adopt it, provided the answer doesn't differ.

Step-by-step explanation: