Question

at what time will a sum amount to 1120 at 4%per annum and 1200% at 5%per annum simple interest?

Answer 1

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.

Answer 2

The formula to find out the amount S, after T years, assuming an interest of R% and principal of P is given as:

S = P + (P x R x T / 100)

The equation with 4% interest is:

1120 = P + (4 x P x T / 100)

The equation with 5% interest is:

1200 = P + (5 x P x T / 100)

Taking both equations:

100 P + 4 PT = 112000
100 P + 5 PT = 120000

  25 P + PT = 28000
- 20 P + PT = 24000
-------------------------
  5 P            = 4000
==============

From this we get P = 800 and P x T = 8000. Hence time taken for initial sum to become the given amounts will be 10 years.