A customer took a loan of Rs. 24,000 at a simple interest rate of 10% per year. At the end of 3 years, the customer settled the loan and interest by handing over a camera valued at Rs. 19,800 and paying the balance in cash. What amount was paid in cash?

Correct Answer: Rs. 11,400

Step-by-Step Explanation:

Step 1: Identify the given values
Principal loan amount ($P$) = Rs. 24,000
Simple interest rate ($R$) = 10% per annum
Time period ($T$) = 3 years

Step 2: Calculate the total Simple Interest (SI) accumulated over 3 years
The standard formula for calculating simple interest is:

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

Substitute the given numerical values into the formula:

$\text{SI}=\frac{24000\times 10\times 3}{100}$

$\text{SI}=240\times 30=\text{Rs. 7,200}$

Step 3: Calculate the total amount required to settle the loan
The total amount ($A$) owed at the end of 3 years is the sum of the principal loan amount and the accumulated simple interest:

$\text{Total Amount (A)}=\text{Principal (P)}+\text{Simple Interest (SI)}$

$\text{Total Amount (A)}=24000+7200=\text{Rs. 31,200}$

Step 4: Find the balance paid in cash
The customer partially settled the total amount owed by handing over a camera valued at Rs. 19,800. The remaining balance was paid in cash:

$\text{Cash Paid}=\text{Total Amount}-\text{Value of Camera}$

$\text{Cash Paid}=31200-19800=\text{Rs. 11,400}$

Therefore, the amount paid in cash was Rs. 11,400.