Question

vivek is older than krish by 5 years .the sum of resiprocals of their ages is 1/6,find their ages.

Answer 1

Answer:

LET VIVEK = X , KRISH = Y

GIVEN :- vivek is older than krish by 5 years

SO, X = 5+Y

SUM OF RECIPROCALS

==> 1/X+1/Y = 1/6

==> Y+X/XY= 1/6

  CROSS MULTIPLY

==> 6(Y+X) = 1(XY)

==> 6Y+6X = XY...(1)

PUTTING VALUE OF X IN EQ(1)

==> 6Y+6(5+Y) = (5+Y)(Y)

==> 6Y+30+6Y = 5Y+Y²

==> 12Y+30 = 5Y+Y²

==> 0 = Y²-12Y+5Y-30

==> 0 = Y²-7Y-30

==>  Y²-10Y+3Y-30 = 0

 ==> Y(Y-10)+3(Y-10) = 0

==> (Y-10) (Y+3) = 0

==> Y = 10 , -3

NEGATIVE ZERO IS NOT POSSIBLE . SO, -3 IS REJECTED

SO, Y = 10

KRISH = 10

AND , X = 5+Y

SO, X = 5+10 ==> 15

  AO, VIVEK = 15 AND KRISH = 10