NIELIT 2018-1

Question

A Professor passed one sixth of his life in childhood, one twelfth in youth, and one seventh more as a bachelor, five years after his marriage a son was born who died four years before his father at half his final age, then what is the age of Professor?

• A. $84$ years
• B. $74$ years
• C. $64$ years
• D. $54$ years

Answer 1

Assuming, Professor's age as $x$ years

Now,

He spends $\dfrac{x}{6}^{th}$ of his life in childhood,

$\qquad \qquad \dfrac{x}{12}^{th}$ in youth,

$\qquad \qquad \dfrac{x}{7}^{th}$ as bachelor,

after $5$ years of his marriage, his son was born & son's age is $\left ( \dfrac{x}{2} - 4  \right )$.

$\therefore x = \dfrac{x}{6} + \dfrac{x}{12} + \dfrac{x}{7} + 5 + \dfrac{x}{2} + 4 \\ Or, x = \dfrac{x}{4} + \dfrac{x}{2} + \dfrac{x}{7} + 9 \\  Or, x = \dfrac{3x}{4} + \dfrac{x}{7} + 9 \\ Or, x = \dfrac{25x}{28} + 9 \\ Or, 3x = 28 \times 9 \\ Or, x = 84 $

$\therefore \text{ 84 years is the Professor's age.}$

Comments

“his son was born & son's age is (x/2−4)”. this line is wrong. his son lived for x/2 years and after that 4 years hence professor died.

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I think the son died and born in the same year.