Multiple choice

Babulal deposited a certain amount of money in a cooperative bank which offers simple interest at a certain rate percent per annum. If the sum becomes five times itself at the end of 30 years, after how many years was the sum double itself?

  1. 5

  2. 6

  3. 6⅔

  4. 7½
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D Correct answer
Explanation

Simple interest formula is A = P(1 + rt). If the sum becomes 5 times itself in 30 years, 5P = P(1 + 30r), so 4 = 30r, meaning r = 4/30 = 2/15. To double the sum, 2P = P(1 + (2/15)t), so 1 = (2/15)t, which gives t = 15/2 = 7.5 years.

AI explanation

If a sum becomes five times itself under simple interest, the interest earned is 4 times the principal over 30 years. Using the simple interest formula, this means 4P = (P * R * 30) / 100, which gives a rate of 40/3 percent. To find when the sum doubles, it must earn 1P in interest, so 1P = (P * 40/3 * T) / 100. Solving for T gives T = 300/40 = 7.5 years.

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