For a certain sum, the amount received after 2 years at 18% p.a. simple interest is Rs.1,100 less than the simple interest on the same sum for 10 years at the same rate. The sum (in Rs.) is:

Given:

Time for amount = 2 years

Rate = 18% per annum

Amount after 2 years is Rs.1100 less than the simple interest for 10 years

Formula used:

Simple Interest (SI) = \( \frac{P \times R \times T}{100} \)

Calculation:

SI for 2 years = \( \frac{P \times 18 \times 2}{100} \) = \( \frac{36P}{100} \)

SI for 10 years = \( \frac{P \times 18 \times 10}{100} \) = \( \frac{180P}{100} \)

According to the question:

Amount after 2 years = Principal + SI for 2 years

\( P + \frac{36P}{100} \) = SI for 10 years - 1100

\( P + \frac{36P}{100} = \frac{180P}{100} - 1100 \)

⇒ \( \frac{136P}{100} = \frac{180P}{100} - 1100 \)

⇒ \( 136P = 180P - 110000 \)

⇒ \( 180P - 136P = 110000 \)

⇒ \( 44P = 110000 \)

⇒ \( P = 2500 \)

∴ The required sum is Rs.2500.