Multiple choice

A man invests a certain sum of money at $6\%\ p.a.$ simple interest and another sum at $7\%\ p.a.$ simple interest. His income from interest after $2$ years was $Rs.\ 354$. One-fourth of the first sum is equal to one-fifth of the second sum. The total sum invested was

  1. $Rs.\ 1500$
  2. $Rs.\ 1200$
  3. $Rs.\ 2700$
  4. $Rs.\ 5400$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let sums be S1 and S2. S1/4 = S2/5 => S2 = 1.25*S1. Interest: (S1 * 0.06 * 2) + (S2 * 0.07 * 2) = 354. 0.12*S1 + 0.14*(1.25*S1) = 354. 0.12*S1 + 0.175*S1 = 354. 0.295*S1 = 354. S1 = 1200. S2 = 1500. Total = 2700.

AI explanation

Let the first sum be x and the second sum be y, where one-fourth of the first sum equals one-fifth of the second sum, giving y = 5x/4. Using the simple interest formula, the total interest after 2 years is (x x 6 x 2)/100 + (y x 7 x 2)/100 = 354. Substituting y gives 12x/100 + 14(5x/4)/100 = 354, which simplifies to 12x/100 + 17.5x/100 = 354, resulting in 29.5x = 35400 and x = 1200. The second sum y is 5 x 1200 / 4 = 1500, making the total sum invested 1200 + 1500 = Rs. 2700.

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