Question

10 years later.A will be twice as old as B and 5 years ago A was 3 times as old as B what will be the present ages​

Answer 1

Step-by-step explanation:

Let the ages of A and B be x and y years respectively.

From first condition

x+10=2(y+10)

x+10=2y+20

x-2y=10...(1)

From second condition

x-5=3(y-5)

x-5=3y-15

x-3y=-10...(2)

eq(1)-eq(2)

y=20

substituting y=20 in eq(1)

x-2(20)=10

x-40=10

x=10+40

x=50

The ages of A and B are 50 and 20 years respectively.

Answer 2

10 years later, A will be twice as old as B.

Let us assume that the present age of A is x years and B is y years.

10 years later, Age of A = (x + 10) years

And the age of B = (y + 10) years

According to question

⇒ (x + 10) = 2(y + 10)

⇒ x + 10 = 2y + 20

⇒ x - 2y = + 20 - 10

⇒ x = 2y + 10

Similarly, 5 years ago A was 3 times as old as B.

5 years ago, Age of A = (x - 5) years

And the age of B = (y - 5) years

According to question,

⇒ (x - 5) = 3(y - 5)

⇒ x - 5 = 3y - 15

⇒ x = 3y - 10

On comparing both the equations, we get

⇒ 2y + 10 = 3y - 10

⇒ 2y - 3y = -10 - 10

⇒ -y = - 20

⇒ y = 20

Substitute value of y in x

⇒ x = 2(20) + 10

⇒ x = 40 + 10

⇒ x = 50

Therefore,

The present age of A is 50 years and B is 20 years.