# 4 years before paul’s age is 3times the alice age and the present age of paul is 2times the alice. what is the present age of paul

4 years before paul’s age is 3times the alice age and the present age of paul is 2times the alice. what is the present age of paul?​

### 2 thoughts on “4 years before paul’s age is 3times the alice age and the present age of paul is 2times the alice. what is the present age of paul”

1. GIVEN :-

• 4 years before , Paul’s age was 3 times Alice’s age.
• Present age of Paul is 2 times Alice age.

TO FIND :-

• Present age of Paul.

SOLUTION :-

Let present age of Paul be ‘x’ years and Alice be ‘y’ years.

CASE 1 —

4 years before , Paul’s age was 3 times Alice’s age.

4 years ago ,

• Paul’s age → ‘x-4’ years
• Alice’s age → ‘y-4’ years

x – 4 = 3(y – 4)

x – 4 = 3y – 12

x – 3y = – 12 + 4

x – 3y = -8 ——(i)

CASE 2 —

Present age of Paul is 2 times Alice age.

x = 2y

y = x/2 ——(ii)

Putting y=x/2 in equation (i),

→ x – 3y = -8

→ x – 3(x/2) = -8

→ x – (3x/2) = -8

→ (2x-3x)/2 = -8

→ -x/2 = -8

→ -x = -8 × 2

→ -x = -16

x = 16

Hence , age of Paul is 16years.

2. let Paul’s age be x and Alice age be y

by first condition

x – 4 = 3(y – 4)

x – 4 = 3y – 12

x = 3y – 8

by second condition

x = 2(y)

3y – 8 = 2y

3y – 2y = 8

y = 8

by substituting y

x = 2y

x = 2(8)

x = 16