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The sum of the reciprocals of the ages of two colleagues is five times the difference of the reciprocals of their ages. If the ratio of the…

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The sum of the reciprocals of the ages of two colleagues is five times the difference of the reciprocals of their ages. If the ratio of the products of their ages to the sum of their ages is 14.4 : 1, the age (in years) of one of the colleagues must be between (both inclusive)
  • A24 years and 36 years
  • B21 years and 23 years
  • C19 years and 21 years
  • D17 years and 21 years
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Suppose that age of the two colleagues be x year and y year

According to question:

⇒ 1/x + 1/y = 5(1/x - 1/y)

⇒ y = 3x/2 - - - - - - - - (i)

Again

⇒ 5xy = 72 (x + y)

⇒ xy/(x + y) = 14.4/1

From equation (i):

⇒ {5x × 3x/2)} = 72 × (x + 3x/2)

⇒ x = 24 year

∴ Age of one of colleagues lies between 24 and 36 year