Question

10 years later a will be twice as old as B and five years ago a was three times as old as B what are the present ages of a and b​

Answer 1

Let A present age be x yrs

" B " " y yrs

A age after 10yrs=x+10

B " " = y+10

ATQ

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

2x+20=y+10

20-10=y-2x

10= y-2x

y= 10+2x -------- (1)

A age 5yrs ago=x-5

B " " " = y-5

ATQ

3(x-5)= y-5

Substituting (1)

3(x-5)= 10+2x-5

3x-15= 2x+5

3x-2x= 15+5

x= 10

Thus, age of A=x= 10yrs

Age of B=y= 10+2x=10+2(10)= 30yrs

Answer 2

A = 50 years

B = 20 years

Step-by-step explanation:

Let the present age of A = x years

Let the present age of B = y years

According to question

10 years later A will be twice as old as B

then,

$x+10=2(y+10)\\x+10=2y+20\\x-2y=10-(i)$

and five years ago A was three times as old B

then,

$x-5=3(y-5)\\x-5=3y-15\\x-3y=-10-(ii)$

Subtracting equation (i) from equation (ii)

after solving,

y = 20 and x = 50

then,

A = 50 years

B = 20 years