#### A certain sum amounts to ₹ 798.60 after 3 years and ₹ 878.46 after 4 years. Find the interest rate and the sum.

**Solution:**

It is given that

Amount after 3 years = ₹ 798.60

Amount after 4 years = ₹ 878.46

So the difference = 878.46 – 798.60 = ₹ 79.86

Here ₹ 79.86 is the interest on ₹ 798.60 for 1 year.

We know that

Rate = (SI × 100)/ (P × t)

Substituting the values

= (79.86 × 100)/ (798.60 × 1)

Multiply and divide by 100

= (7986 × 100 × 100)/ (79860 × 100 × 1)

= 10%

Here

A = P (1 + r/100)^{n}

It can be written as

P = A ÷ (1 + r/100)^{n}

Substituting the values

P = 798.60 ÷ (1 + 10/100)^{3}

By further calculation

P = 79860/100 × 10/11 × 10/11 × 10/11

P = ₹ 600

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