Question

Vivek is older than Kishor by 5 years. The sum of the reciprocals of their ages is 1/6. Find their present ages.Solve the word problem

Answer 1

Let Vivek's age is X years
and Kishor's age is Y years

A/C to question,
Vivek is older than Kishorby 5 years
e.g., X = 5 + Y ------(1)

sum of reciprocal of their age is 1/6
e.g., 1/X +1/Y = 1/6 -----(2)

put equation (1) in equation (2),
1/(5 + Y) + 1/Y = 1/6
=> (Y + 5 + Y)/(5 + Y)Y = 1/6
=> (5 + 2Y)/(5Y + Y²) = 1/6
=> 6(5 + 2Y) =5Y + 2Y²
=> 30 + 12Y = 5Y + 2Y²
=> 2Y² - 7Y - 30 =0
=> 2Y² - 12Y + 5Y - 30 = 0
=> 2Y(Y - 6) + 5(Y - 6) = 0
=> (2Y + 5)(Y - 6) = 0
=> Y = 6 and -5/2
but age can't be negative
so, Y ≠-5/2 hence, Y = 6 , put it in equation (1)
X =5 + Y = 5 + 6 = 11

hence, Vivek's age = 11 years
Kishor's age = 6 years