please solve this question.
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Answers
Step-by-step explanation:
Let the present age of A and B be x and y.
5 year ago,
(x-5)=3(y-5)
x-5=3y-15
x-3y=-10-----------(i)
10 years later,
(x+10)=2(y+10)
x+10=2y+20
x-2y=10---------(ii)
#subtracting i- ii
x-3y-x+2y=-10-10
-y= -20
y=20
x=10+2(20)
=50
so the age of
A=50 years....
B=20 years......
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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:
The present age of A is 50 years.
And the present age of B is 20 years.
Step-by-step-explanation:
Let the present age of A be x years.
And the present age of B be y years.
Five years ago,
Age of A = ( x - 5 ) years
Age of B = ( y - 5 ) years
From the first condition,
( x - 5 ) = 3 ( y - 5 )
⇒ x - 5 = 3y - 15
⇒ x - y = - 15 + 5
⇒ x - y = - 10 - - ( 1 )
Now, ten years after,
Age of A = ( x + 10 ) years
Age of B = ( y + 10 ) years
From the second condition,
( x + 10 ) = 2 ( y + 10 )
⇒ x + 10 = 2y + 20
⇒ x - 2y = 20 - 10
⇒ x - 2y = 10 - - ( 2 )
Now, by subtracting equation ( 1 ) from equation ( 2 ), we get,
x - 2y = 10 - - ( 2 )
-
x - 3y = - 10 - - ( 1 )
(-)... (+)..... (+)
_____________
⇒ y = 20
By substituting y = 20 in equation ( 2 ), we get,
x - 2y = 10 - - ( 2 )
⇒ x - 2 × 20 = 10
⇒ x - 40 = 10
⇒ x = 10 + 40
⇒ x = 50
Now,
Present age of A ( x ) = 50 years.
Present age of B ( y ) = 20 years.