Multiple choice

Ram divided $2189$ in three parts such that interest on them after $1,2$ and $3$ years respectively be equal. The rate of $SI$ is $4\%$ per annum in all cases. The smallest part is

  1. $Rs.\ 702$
  2. $Rs.\ 398$
  3. $Rs.\ 425$
  4. $Rs.\ 756$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let the parts be P1, P2, P3. Interest = P*R*T/100. 4*1*P1/100 = 4*2*P2/100 = 4*3*P3/100. P1 = 2P2 = 3P3. P1:P2:P3 = 6:3:2. Total parts = 11. Smallest part = (2/11) * 2189 = 2 * 199 = 398.

AI explanation

Let the three parts be P1, P2 and P3, and their equal simple interest be x, so P1 = x / (R), P2 = x / (2R) and P3 = x / (3R). This means the ratio of the parts P1 : P2 : P3 is 1/1 : 1/2 : 1/3, which is 6 : 3 : 2. The smallest part is represented by 2 units out of a total of 11 units, making it 2/11 of Rs. 2189. Calculating (2/11) * 2189 gives the smallest part as Rs. 398.

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