In what time will ₹10,000 at 4% per annum, produce the same interest as ₹8,000 does in 4 years at 5% simple interest?

To solve this, we first need to find the interest earned by ₹8,000 at 5% simple interest over 4 years.

The formula for simple interest is:

[ text{Interest} = frac{P times R times T}{100} ]

Where:

– ( P = 8000 ) (Principal)

– ( R = 5 ) (Rate of interest)

– ( T = 4 ) (Time in years)

Calculating the interest:

[ text{Interest} = frac{8000 times 5 times 4}{100} ]

[ text{Interest} = frac{80000}{100} ]

[ text{Interest} = 800 ]

So, ₹8,000 at 5% over 4 years produces ₹800 in interest.

Now, we need to find out how much time it will take for ₹10,000 at 4% per annum to produce the same ₹800 in interest.

Using the simple interest formula again:

Let ( T ) be the time in years for ₹10,000 at 4% to produce ₹800 interest.

[ 800 = frac{10000 times 4 times T}{100} ]

[ 800 = 10000 times 0.04 times T ]

[ 800 = 400 times T ]

Now, solving for ( T ):

[ T