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Q.

Vivek is older than Kishor by 5 years. The sum of the reciprocal of their ages is $\frac{1}{6}$ . Find their present ages.

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a

15

b

23

c

34

d

45

answer is A.

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Detailed Solution

Concept- Assume the present age of Kishor as x then age of Vivek will be x+5. Sum of reciprocal of their ages is given using which we can make linear equations and by solving that we can get their present ages.
Assume that the present age of Kishor is x years.
Vivek is older than Kishor by 5 years.
So, Vivek's ag will be

x + 5

The sum of the reciprocals of their age is

\frac{1}{6}

\frac{1}{x}

+

\frac{1}{x + 5}

=

\frac{1}{6}

\frac{x + 5 + x}{x (x + 5)}

=

\frac{1}{6}

\frac{5 + 2 x}{(2 x^{2} + 5 x)}

=

\frac{1}{6}

30 + 12 x = x^{2} + 5 x

x^{2} - 7 x - 30 = 0

x^{2} - 10 x + 3 x - 30 = 0

x (x - 10) + 3 (x - 10) = 0

(x + 3) (x - 10) = 0

x = - 3, 10

Age cannot be in negative so, age of Kishore is 10 years and that of
Vivek is 10+5=15 years old.
Hence, the correct option is 1.

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Vivek is older than Kishor by 5 years. The sum of the reciprocal of their ages is 16. Find their present ages.