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Q.

The sum of the reciprocals of Meena's ages (in years) 3 years ago and 5 years hence is $\frac{1}{3}$ . Then, her present age (in years) is?

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a

10

b

6

c

7

d

9

answer is C.

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Detailed Solution

detailed_solution_thumbnail

Given that the sum of the reciprocals of Meena's ages (in years) 3 years ago and 5 years hence is

\frac{1}{3}

.
Let’s consider that Meena's present age is

y

years.
Then,
3 years Ago,
Meena’s age =

y - 3

After 5 years,
Meena’s age

= y + 3

According to the given condition,

⟹ \frac{1}{y - 3} + \frac{1}{y + 5} = \frac{1}{3}

⟹ \frac{(y + 5) + (y - 3)}{(y - 3) (y + 5)} = \frac{1}{3}

⟹ \frac{y + 5 + y - 3}{y (y + 5) - 3 (y + 5)} = \frac{1}{3}

⟹ \frac{2 y + 2}{y^{2} + 5 y - 3 y - 15} = \frac{1}{3}

⟹ \frac{2 y + 2}{y^{2} + 2 y - 15} = \frac{1}{3}

⟹ 3 (2 y + 2) = y^{2} + 2 y - 15

⟹ 6 y + 6 = y^{2} + 2 y - 15

⟹ y^{2} + 2 y - 6 y - 15 - 6 = 0

⟹ y^{2} - 4 y - 21 = 0

⟹ y^{2} - 7 y + 3 y - 21 = 0

⟹ y (y - 7) + 3 (y - 7) = 0

⟹ (y + 3) (y - 7) = 0

⟹ y + 3 = 0 or y - 7 = 0

∴ y = - 3 or y = 7

∴

Meena’s present age is 7.
Hence, the correct option is 3.

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