Multiple choice

Directions: Given below is a question followed by three statements I, II and III. Read the question and the statements carefully and choose your answer according to the set of statement(s) which is/are sufficient to answer the question. What is the principal amount? I. The sum becomes double in 10 years at 10% per annum simple interest. II. The compound interest obtained on the principal is 1830.4 after two years at the rate of 8% compounded annually. III. The simple interest obtained on the principal after 2 years at 8% rate of interest is 70.4 less than the compound interest obtain on the same principal after 2 years at 8% per annum.

  1. Only II

  2. Only III

  3. Either I or II

  4. Either II or III

  5. All of these
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Statement II provides enough info to find the principal using the compound interest formula for 2 years. Statement III provides the difference between CI and SI for 2 years, which is also sufficient to find the principal using the formula P(r/100)^2. Statement I is also sufficient.

AI explanation

From statement I, using the simple interest formula P = (S.I. * 100) / (R * T), a sum doubling means the interest equals the principal, so P = (P * 100) / (10 * 10), which yields no specific value. Statement II gives the compound interest directly as Rs. 1830.4, allowing you to find the exact principal using the formula P = C.I. / ((1 + R/100)^T - 1). Statement III gives the difference between compound interest and simple interest for two years as Rs. 70.4, and since the principal can also be uniquely found using the difference formula P = Difference * 100^2 / R^2, either statement II or III is sufficient.

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