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?

The correct answer is 4 years.

We need to find the time in which ₹10,000 at 4% per annum produces the same interest as ₹8,000 does in 4 years at 5% simple interest.

Step 1: Calculate the interest earned by ₹8,000 in 4 years at 5% per annum (Simple Interest).

The Simple Interest formula is:

\mathrm{SI}=\frac{P\times R\times T}{100}

Where:
P = Principal = ₹8,000
R = Rate = 5% per annum
T = Time = 4 years

Substituting the values:

\mathrm{SI}=\frac{8000\times 5\times 4}{100}=\frac{160000}{100}=\mathrm{₹1,600}

So, the interest produced by ₹8,000 is ₹1,600.

Step 2: Find the time (T) for ₹10,000 at 4% per annum to produce the same interest of ₹1,600.

Using the same Simple Interest formula and solving for T:

T=\frac{\mathrm{SI}\times 100}{P\times R}

Where:
SI = ₹1,600 (the target interest we just calculated)
P = ₹10,000
R = 4% per annum

Substituting the values:

T=\frac{1600\times 100}{10000\times 4}=\frac{160000}{40000}=4\text{years}

Conclusion: ₹10,000 at 4% per annum will produce the same interest (₹1,600) as ₹8,000 at 5% in 4 years, in exactly 4 years.