Kabir paid 9,600 as interest on a loan he took for 5 years at 16% rate of simple interest. What was the amount of loan he took?
Explanation:
To find the principal amount (loan amount), we use the formula for Simple Interest (SI): $SI = \frac{P \times R \times T}{100}$, where $P$ is the Principal, $R$ is the Rate of Interest, and $T$ is the Time. \nGiven values are: $SI = 9600$ $R = 16\%$ $T = 5$ years \nSubstitute these values into the formula: $9600 = \frac{P \times 16 \times 5}{100}$ \nNow, solve for $P$: $9600 = \frac{P \times 80}{100}$ $P = \frac{9600 \times 100}{80}$ $P = \frac{960000}{80}$ $P = 12000$ \nSo, the amount of loan Kabir took was $12,000$. \nLet's analyze the options:\nOption (A) $16,000$: If the principal were $16,000$, the interest would be $\frac{16000 \times 16 \times 5}{100} = 160 \times 80 = 12800$, which is incorrect.\nOption (B) $12,400$: If the principal were $12,400$, the interest would be $\frac{12400 \times 16 \times 5}{100} = 124 \times 80 = 9920$, which is incorrect.\nOption (C) $12,000$: This matches our calculated principal amount, as $\frac{12000 \times 16 \times 5}{100} = 120 \times 80 = 9600$. This is correct.\nOption (D) $15,600$: If the principal were $15,600$, the interest would be $\frac{15600 \times 16 \times 5}{100} = 156 \times 80 = 12480$, which is incorrect. \nTherefore, the correct option is (C).