John is 3 times as old as peter .in 6 years time john will be twice as old as peter will be . Determine their present ages

Answer 1

J = Present John's age

P = Present Peter's age

John is 3 times as old as peter mean:

J = 3 P

After 6 years John will be J + 6 yrs old

Peter will be P + 6 yrs old

In 6 years time john will be twice as old as peter will be mean:

( J + 6 ) / ( P + 6 ) = 2

Replace J = 3 P in this equation.

( 3 P + 6 ) / ( P + 6 ) = 2

Multiply both sides by P + 6

3 P + 6 = 2 ∙ ( P + 6 )

3 P + 6 = 2 ∙ P + 2 ∙ 6

3 P + 6 = 2 P + 12

Subtract 2 P to both sides

3 P - 2 P + 6 = 2 P - 2 P + 12

P + 6 = 12

Subtract 6 to both sides

P + 6 - 6 = 12 - 6

P = 6 yrs old

J = 3 P = 3 ∙ 6 = 18 yrs old

Proof:

J / P = 18 / 6 = 3

( J + 6 ) / ( P + 6 ) = ( 18 + 6 ) / ( 6 + 6 ) = 24 / 12 = 2