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Five years ago, A was thrice as old as B and ten years later, A shall be twice as old as B. What is the present age of A.
(a) 20(b) 50(c) 60(d) 40?
(a) 20(b) 50(c) 60(d) 40?
Most Upvoted Answer
Five years ago, A was thrice as old as B and ten years later, A shall ...
Problem: Five years ago, A was thrice as old as B and ten years later, A shall be twice as old as B. What is the present age of A?
Solution:
Let the present age of A be x and the present age of B be y.
Five years ago, A was thrice as old as B.
⇒ (x - 5) = 3(y - 5)
⇒ x - 5 = 3y - 15
⇒ x - 3y = -10 ……(1)
Ten years later, A shall be twice as old as B.
⇒ (x + 10) = 2(y + 10)
⇒ x + 10 = 2y + 20
⇒ x - 2y = 10 ……(2)
On solving equations (1) and (2), we get:
x = 50
Therefore, the present age of A is 50.
Solution:
Let the present age of A be x and the present age of B be y.
Five years ago, A was thrice as old as B.
⇒ (x - 5) = 3(y - 5)
⇒ x - 5 = 3y - 15
⇒ x - 3y = -10 ……(1)
Ten years later, A shall be twice as old as B.
⇒ (x + 10) = 2(y + 10)
⇒ x + 10 = 2y + 20
⇒ x - 2y = 10 ……(2)
On solving equations (1) and (2), we get:
x = 50
Therefore, the present age of A is 50.
Community Answer
Five years ago, A was thrice as old as B and ten years later, A shall ...
Let the present age of A be x years.
and present age of B be y years
Five years ago,
age of A = ( x - 5 ) years
age of B = ( y - 5 ) years
according to questions ,
3( y - 5 ) = ( x - 5 )
or. 3y - 15 = x - 5
or. 3y - x = 15 - 5
or. 3y - x = 10. .( i )
Ten years later ,
age of A = ( x + 10 ) years
age of B = ( y + 10 ) years
according to questions ,
2 ( y + 10 ) = ( x + 10 )
or. 2y + 20 = x + 10
or. 2y - x = 10 - 20
or. x - 2y = 10. .( ii )
multiply equation ( i ) by 2 and equation ( ii ) by 3
6y - 2x = 20
-6y + 3x = 30
after addition we get ,
x = 50
hence , present age of A is 50 years
and present age of B be y years
Five years ago,
age of A = ( x - 5 ) years
age of B = ( y - 5 ) years
according to questions ,
3( y - 5 ) = ( x - 5 )
or. 3y - 15 = x - 5
or. 3y - x = 15 - 5
or. 3y - x = 10. .( i )
Ten years later ,
age of A = ( x + 10 ) years
age of B = ( y + 10 ) years
according to questions ,
2 ( y + 10 ) = ( x + 10 )
or. 2y + 20 = x + 10
or. 2y - x = 10 - 20
or. x - 2y = 10. .( ii )
multiply equation ( i ) by 2 and equation ( ii ) by 3
6y - 2x = 20
-6y + 3x = 30
after addition we get ,
x = 50
hence , present age of A is 50 years
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Five years ago, A was thrice as old as B and ten years later, A shall be twice as old as B. What is the present age of A.(a) 20(b) 50(c) 60(d) 40?
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