Question

six yers ago the ratio of the age of the two person P and Q was 3:2 .four years of the ratio of their age will be 8:7 .what's is P's age​

Answer 1

Solution :-

Let the age be x and y

Six years ago, The ratio of the age of the two person P and Q was 3 : 2

According to the question,

The age of P and Q six year's ago

( x - 6 ) / (y - 6 ) = 3/2

By cross multiply,

2(x - 6 ) = 3 ( y - 6 )

2x - 12 = 3y - 18

2x = 3y - 18 + 12

2x = 3y - 6

x = 3y - 6 / 2 eqn( 1 )

Four years later the ratio of their age will be 8 : 7

Therefore,

( x + 4 ) / ( y + 4 ) = 8/ 7

By cross multiply,

7( x + 4 ) = 8( y + 4 )

7x + 28 = 8y + 32

7x = 8y + 32 - 28

7x = 8y + 4

7x = 8y + 4 eqn( 2 )

Subsitute the value of x in eqn(2)

7( 3y - 6 / 2 ) = 8y + 4

7(3y - 6 /2 ) = 8y + 4

21y - 42/ 2 = 8y + 4

21y - 42 = 16y + 8

21y - 16y = 8 + 42

5y = 50

y = 10

Now , Subsitute the value of y in eqn( 1 )

x = 3y - 6 / 2

x = 3 ( 10 ) - 6 / 2

x = 30 - 6 / 2

x = 24/2

x = 12

Hence, The present age of P and Q is 12 and 10 years $.$

Answer 2

Given

• Six years ago, ratio of two persons (P and Q) = 3 : 2
• Four years later the ratio these persons = 8 : 7

To find

• Present ages of P and Q

Solution

Let the ages of P and Q be x and y,

The age of P and Q six years ago :-

• (x - 6) / (y - 6) = 3 / 2

The age of P and Q four years later :-

• (x + 4) / (y + 4) = 8/ 7

Let's solve these :-

• 2(x - 6) = 3 (y - 6)

• 2x - 12 = 3y - 18

• 2x = 3y - 18 + 12

• 2x = 3y - 6

• x = 3y - 6/2  (i)

• 7(x + 4) = 8(y + 4)

• 7x + 28 = 8y + 32

• 7x - 8y = 32 - 28

• 7x - 8y = 4

• 7x = 8y + 4   (ii)

Substitute the value of x in (ii)

• 7(3y - 6/2) = 8y + 4

• 21y - 42/2 = 8y + 4

• 21y - 16y = 8 + 42

• 5y = 50

• y = 50/5

• y = 10

Hence, the value of y is 10, substitute in (i) and let's find x,

• x = 3y - 6/2

• x = 3(10) - 6/2

• x = 30 - 6/2

• x = 24/2

• x = 12

Hence the value of x is 12

Therefore the present ages of P is 12 years and Q is 10 years.