Question

14. Two years ago, Dilip was three times as old as
his son find two years hence, twice his age will
be equal to five times that of his son. The
present age of son and Dilip are
(a) 14 yr, 38 yr
(b) 16 yr, 40 yr
(c) 12 yr, 36 yr
(d) None of these ​

Answer 1

Given that,

• Two years ago, Dilip was three times as old as his son.

⠀⠀⠀

Therefore,

• Age of Son is x
• Age of Dilip is 3x

Now,

• The present age of son be (x + 2).
• And, the present age of Dilip be (3x + 2).

⠀⠀⠀

☯ After two years,

$:\implies\sf Son's \: age = (x + 2 + 2) = x + 4$

$:\implies\sf Dilip's \: age = (3x + 2 + 2) = 3x + 4$

⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━━━⠀

⠀⠀

⠀⠀⠀⠀$\underline{\bigstar\:\boldsymbol{According\:to\:the\:question\::}}$

$:\implies\sf 5(x + 4) = 2(3x + 4) \\\\\\:\implies\sf 5x + 20 = 6x + 8 \\\\\\:\implies\sf 5x - 6x = 8 - 20\\\\\\:\implies\sf -x = - 12\\\\\\:\implies{\underline{\boxed{\frak{\purple{x = 12}}}}}\bigstar$

Hence,

• Present age of son, (x + 2) = 14 years.
• Present age of Dilip, (3x + 2) = 24 + 14 = 38 years.

⠀⠀⠀

$\therefore\:{\underline{\sf{Option (a) \ is \ correct.}}}$

⠀⠀

$\therefore\:{\underline{\sf{Hence, \ The \ present \ age \ of \ son \ and \ Dilip \ is \ {\textsf{\textbf{14, 38 years.}}}.}}}$

Answer 2

Answer:

Given :-

• Two years ago, Dilip was three times as old as his son and after two years their age will be twice of his age will be equal to five times that of his son.

To Find :-

• What is the present age of son and Dilip.

Solution :-

Let, the age of son be x

And, the age of Dilip will be 3x

➙ Hence,

Present age of son be x + 2

And, the present age of Dilip is 3x + 2

➙ After two years,

Age of son is x + 4

And, the age of Dilip will be 3x + 4

➤ According to the question,

⇒ 2(3x + 4) = 5(x + 4)

⇒ 6x + 8 = 5x = 20

⇒ 6x - 5x = 20 - 8

➠ x = 12

Hence, their present ages are,

✧ Present age of son = x + 2 = 12 + 2 = 14 years

✧ Present age of Dilip = 3x + 2 = 3(12) + 2 = 36 + 2 = 38 years

∴ The present age of son is 14 years and the present age of Dilip is 38 years .

Hence, the correct options is option no (a) 14 yrs, 38 yrs.

$\rule{150}{1}$

Let's Verify :-

↦ 2(3x + 4) = 5(x + 4)

↦ 6x + 8 = 5x + 20

Put x = 12 we get,

↦ 6(12) + 8 = 5(12) + 20

↦ 72 + 8 = 60 + 20

↦ 80 = 80

➦ LHS = RHS

Hence, Verified ✔