Multiple choice

A lent B Rs. 900 for a certain time at a certain rate per annum which was equal to the square root of the number of months of time. After the time, B wanted to return the money, but A instead of taking the interest, which amounted to Rs. 48, asked for a certain sum of money at the same rate for a certain number of years which was equal to the square root of the rate. Find the sum of money so that neither of them ends up as a loser. (Take simple interest)

  1. Rs. 720

  2. Rs. 640

  3. Rs. 600

  4. Rs. 580
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let time be T months, rate be R% per annum. R = sqrt(T). Interest = (P * R * T_years) / 100. 48 = (900 * R * (T/12)) / 100. Substituting T = R^2, 48 = 9 * R * (R^2/12) = 0.75 * R^3. R^3 = 64, so R = 4. T = 16 months. The second part involves finding a sum P2 such that interest is equal. This leads to P2 = 600.

AI explanation

Using the simple interest formula SI = P * R * T / 100 with the initial principal of Rs. 900, we have 48 = 900 * R * T / 100, where the rate R is the square root of the months of time T. Since the time in months equals R squared, substituting T = R squared makes the rate equal to 4%. To ensure neither loses, the new principal must generate Rs. 48 in interest at 4% for 2 years, so 48 = P * 4 * 2 / 100, which results in a sum of Rs. 600.

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