Multiple choice

Divide Rs. $793$ into three parts such that their amounts after $2, 3$ and $4$ years may be equal, the rate of interest being $5\%$. The ratio between these parts will be

  1. $10:15:20$
  2. $110:115:120$
  3. $\displaystyle\frac{1}{10}:\frac{1}{15}:\frac{1}{20}$
  4. $\displaystyle\frac{1}{110}:\frac{1}{115}:\frac{1}{120}$
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D Correct answer
Explanation

Let the parts be P1, P2, P3. Amounts are P1(1 + 0.05*2) = P2(1 + 0.05*3) = P3(1 + 0.05*4). This is 1.10P1 = 1.15P2 = 1.20P3. The ratio P1:P2:P3 is 1/1.10 : 1/1.15 : 1/1.20.

AI explanation

Let the three parts be x, y, and z, and their equal amount after the given time periods be A. Using the simple interest formula, the principal equals 100 times A divided by 100 plus rate times time, so x is 100A divided by 110, y is 100A divided by 115, and z is 100A divided by 120. The ratio of x to y to z is therefore 100 divided by 110 to 100 divided by 115 to 100 divided by 120, which simplifies to 1 divided by 110 to 1 divided by 115 to 1 divided by 120.

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