Multiple choice

A person has left an amount of Rs. 1,20,000 to be divided between his two sons, aged 14 years and 12 years such that they get equal amounts when each attains 18 years of age. If the amount gets a simple interest of 5% per annum, the younger son's share at present is

  1. Rs. 48,800

  2. Rs. 57,600

  3. Rs. 62,400

  4. Rs. 84,400
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let younger son's share be x, older be y. x + y = 120000. Younger son (12) gets amount at 18 (6 years interest). Older son (14) gets amount at 18 (4 years interest). x(1 + 0.05*6) = y(1 + 0.05*4) => 1.3x = 1.2y => y = 1.3x/1.2 = 13x/12. x + 13x/12 = 120000 => 25x/12 = 120000 => x = 120000 * 12 / 25 = 57600.

AI explanation

Let the present shares of the 14-year-old and 12-year-old sons be x and (120000 - x) respectively. Using the simple interest formula A = P + (P * R * T)/100, their final amounts are x + (x * 5 * 4)/100 = 1.2x and (120000 - x) + ((120000 - x) * 5 * 6)/100 = 1.3(120000 - x). Equating the two amounts gives 1.2x = 156000 - 1.3x, which simplifies to 2.5x = 156000, making the younger son's present share (120000 - 62400) equal to Rs. 57,600.

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