Question

Jack's present age is one fourth of his father's age two years ago.
Jack's father's age will be twice Raman's age after 10 years. If
Raman's 12th birthday was celebrated 2 years ago, then what is
Jack's present age?​

Answer 1

Let the present age of Jack be x years

Let the present age of Jack's father be y years.

Let the present age of Raman be z years.

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⠀⠀⠀⠀ ☯ According to the Question

Jack's present age is one fourth of his father's age two years ago.

$:\implies$ x = (y-2)/4 --------------(i)

Jack's father's age will be twice Raman's age after 10 years.

$:\implies$ y + 10 = 2(z + 10) -------------(ii)

Raman's 12th birthday was celebrated 2 years ago.

$:\implies$ z = 14 (z-2 = 12 = 14) ----------(iii)

Now, Substitute the value of z =14 in equation (ii) we get

$\longmapsto$ y + 10 = 2(14+10)

$\longmapsto$ y +10 = 2(24)

$\longmapsto$ y+10 = 48

$\longmapsto$ y = 48-10

$\longmapsto$ y = 38

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Now,

Substitute the value of y = 38 in equation (i) we get

$\longrightarrow$ x = (38-2)/4

$\longrightarrow$ x = 36/4

$\longrightarrow$ x = 9

• Hence, the Present age of Jack is 9 years.

Answer 2

Answer:

Given :-

Jack's present age is one fourth of his father's age two years ago. Jack's father's age will be twice Raman's age after 10 years. If Raman's 12th birthday was celebrated 2 years ago,

To Find :-

Jack's present age

Solution :-

Let

Present age of Jack = a

Present age of Jack's father = b

Now

ATQ

a = (b - 2)/4

4a = b - 2 (1)

Age of Jack's father =

b + 10 = 2(12 + 2 + 10)

b + 10 = 2(24)

b + 10 = 48

b = 48 - 10

b = 38 years

By using first equation

4a = 38 - 2

4a = 36

a = 36/4

a = 9 years