Multiple choice

In the given question, a question is asked and is followed by three statements.While answering the question, you may or may not require the data provided in all the statements.You have to read, the question and the three statements and then decide whether the question can be answered with any one or two of the statements or all the three statements are required to answer the question.Select the correct option.What is the Principal sum ? (i) The sum amounts to Rs.690 in 3 years at S.I (ii) The sum amounts to Rs.750 in 5 years at S.I (iii) The rate of interest is $5\%$ p.a

  1. Both (i) and (iii)

  2. Both (ii) and (iii)

  3. Both (i) and (ii)

  4. Any two of the three
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Simple Interest (SI) = P * R * T / 100. (i) 690 = P + P * R * 3 / 100. (ii) 750 = P + P * R * 5 / 100. (iii) R = 5. With any two statements, we have two variables (P and R) or can solve for P using the difference in interest over time.

AI explanation

Using statements I and II, the interest for two years is the difference between the amounts, 750 - 690 = 60, leading to a yearly interest of 30 and a principal of 690 - 90 = 600. Using statements I and III with the simple interest formula, 690 = P + P * 5 * 3 / 100, we solve to find the principal is 600. Using statements II and III, 750 = P + P * 5 * 5 / 100 also gives the principal as 600. Because any two of the three equations mathematically lock in both the unknown principal and the rate of interest, any two of the three statements are required.

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