Question

Five years ago, A was thrice as old as B and ten years later, A shall be twice as old as B. What are the present ages of A and B?

Answer 1

Answer:

15 and 35

Step-by-step explanation: 5 years back,

A=10

B=30

AFTER 10 YEARS,

A=20

B=40

Answer 2

Given:-

• Five years ago, A was thrice as old as B
• Ten years later, A shall be twice as old as B

To find:-

• Find is the present age of A and B ...?

Solution:-

Five years ago, A was thrice as old as B

• A's age = (x - 5)
• B's age = (y - 5)

According to the question:-

=> (x - 5) = 3(y - 5)

=> x - 5 = 3y - 15

=> x - 3y = -15 + 5

=> x - 3y = -10

=> x = 3y - 10 ........(i).

Ten years later, A shall be twice as old as B

• A's age = (x + 10)
• B's age = (y + 10)

According to the question:-

=> (x + 10) = 2(y + 10)

=> x + 10 = 2y + 20

=> x - 2y = 20 - 10

=> x - 2y = 10 ..........(ii).

Now, putting the value of 'x' from equation (ii) in equation (i).

=> x - 2y = 10

=> 3y - 10 - 2y = 10

=> 3y - 2y = 10 + 10

=> y = 20

• Present age of B = y = 20 years

Putting the value of 'y' in equation (i).

=> x = 3y - 10

=> x = 3 × 20 - 10

=> x = 60 - 10

=> x = 50

• Present age of A = x = 50 years

Hence, the present age of 'A' is 50 years and the present age of 'B' is 20 years.