Question

. The sum of the present ages of P and Q is 84 years.
Six years ago, the age of P was twice that of Q.
What is the difference between the present ages
of P and Q?

Answer 1

question❓

The sum of the present ages of P and Q is 84 years.

Six years ago, the age of P was twice that of Q.

What is the difference between the present ages

of P and Q?

Answer:24

★explanation

★Solution goes as :

★6 Years ago :

let age of Q be ‘x’

then age of P would have been ‘2x’ (6 years ago condition)

★Present :

Age of Q has become ‘x+6’

Age of P has become ‘2x+6’

★Sum of their present ages is : (x+6) + (2x+6) = 84

The above equation gives x=24

So the present age of P = 2x+6 = 54

and present age of Q = x+6 = 30

★Giving the present difference of ages = 24

Answer 2

To Find:-

• Find the difference between the present ages of P and Q.

Given:-

• The sum of the present ages of P and Q is 84 years.
• Six years ago, the age of P was twice that of Q.

Solution:-

Let the age of Q be " x + 6 "

Then the age of P be " 2x + 6 "

$\tt\implies \: ( x + 6 ) + ( 2x + 6 ) = 84$

$\tt\implies \: x + 6 + 2x + 6 = 84$

$\tt\implies \: 3x + 12 = 84$

$\tt\implies \: 3x = 84 - 12$

$\tt\implies \: 3x = 72$

$\tt\implies \: x = \dfrac { 72 } { 3 }$

$\tt\implies \: x = 24$

Hence,

$\tt \: The \: present \: of \: Q \: is \: x + 6 = 24 + 6 = 30$

$\tt \: Then \: present \: age \: of \: P \: is \: 2x + 6 = 2( 24 ) + 6 = 54$

Now,

$\tt\implies \: P - Q$

$\tt\implies \: 54 - 30$

$\tt\implies \: 24$