Five years ago, A was thrice as old as B and 10 years later, A shall be twice as old as B. What are the present ages of A and B?

Explanation

Let the present ages of B and A be x years and y years respectively. Then ,
B's age 5 years ago = `( x- 5) ` years .
and A's age 5 years ago = ( y - 5) years.
` therefore (y - 5) = 3 ( x - 5) rArr 3x - y = 10" " `... (i)
B's age 10 years hence = (`x + 10 `) years.
A's age 10 years hence = ` ( y + 10)` years.
` therefore ( y + 10 ) = 2 ( x + 10 )rArr 2 x - y = - 10 " " `... (ii)
On substracting (ii) from (i), we get x = 20
Putting x = 20 in (i), we get
` ( 3 xx 20 ) - y = 10 rArr y = 60- 10 = 50 `
`therefore x = 20 and y = 50 ` Hence, B's present age = 20 years.
and A's present age = 50 years.