Question

Sonam is 3 years elder than Sujata.The sum of the reciprocal of their ages is 3/20 . Find their ages​

Answer 1

Let the age of Sonam = x

Let the age of Sujata = y

Given,

Sonam's age = Sujata + 3

=> x = y+3..............( a)

1/x + 1/y = 3/20

y + x/ xy = 3/20

20y + 20x = 3xy

substituting the value of x,

20 y + 20( y+3) = 3 y( y+3)

20y + 20y + 60 = 3y² + 9y

3y² - 31y -60 = 0

3y² - 36y +5 y -60 = 0

3y( y -12) +5( y -12) = 0

taking (y-12),

y -12 = 0

y = 12

thus,

Sujata's age = 12 years

Sonam's age = 15 years