Multiple choice

If we divide Rs. 1870 into three parts in the ratio 2 : x : y, then 2, x, y are in harmonic progression and x, y add up to 9. What amount will add up to x and y?

  1. Rs. 1340

  2. Rs. 1470

  3. Rs. 1530

  4. Rs. 1620
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Ratio 2 : x : y. Harmonic progression means 1/2, 1/x, 1/y are in AP. So 2/x = 1/2 + 1/y. Given x + y = 9, y = 9 - x. Substitute: 2/x = (y+2)/2y = (11-x)/(18-2x). Solving gives x=6, y=3. The parts are 2k, 6k, 3k. Total = 11k = 1870, k = 170. x+y = 9k = 9 * 170 = 1530.

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