Q4: Barry's age is twice that of Clyde. Five years
ago Barry was three times older than Clyde. Find
the age of both.
Answers
Given :-
Barry's present age is twice that of Clyde.
Five years ago, Barry was three times older than Clyde.
To Find :-
Age of both.
Solution :-
Let the present ages of Barry and Clyde be x and y respectively.
According to the question, There are two conditions of different time :-
Case 1 (Present)
Barry's present age is twice that of Clyde.
This can be expressed as,
⇒ x = 2y
⇒ x - 2y = 0 ...(i)
Let's find the other linear equation in two variables with the help of the second case,
Case 2 (Past , 5 years ago)
Because this condition holds true 5 years ago hence 5 must be subtracted from both ages.
⇒ (Barry's age - 5) = 3(Clyde's age - 5)
⇒ x - 5 = 3(y - 5)
⇒ x - 5 = 3y - 15
⇒ x - 3y = -10 ...(ii)
Subtracting (ii) from (i), [ As the coefficient of x is same in both the equations, Hence subtracting the equations would eliminate x from the resultant equation and then we can find the value of y ]
⇒ x - 2y - (x - 3y) = 0 -(-10)
⇒ x - 2y - x + 3y = 10
⇒ 3y - 2y = 10
⇒ y = 10
Substitute value of y in eq.(i), we get x
⇒ x - 2y = 0
⇒ x = 2(10)
⇒ x = 20
Hence, Present age of Barry is 20 years while that of Clyde is 10 years.
Answer:
ago Barry was three times older than Clyde. Find
the age of both.