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 1

in image last part has some mistake.correct one is
x-2y=10
x-2×20=10
x-40=10
x=10+40
x=50 years
hence present age of "a" is 50 years & "b" is 20 years.

Answer 2

Answer:

Present age of a = 50 years and of b = 20 years

To find:

Present ages of a and b = ?

Solution:

Given :  

1. Five years ago a was three times as old as b  

2. Ten years later a shall be twice older than b.

Assume that present age of a as x and that of b as y.

Five years ago, a was thrice as old as b  

i.e. age of a was x - 5 and age of b was 3(y-5)

x - 5 = 3 (y - 5)

x - 5 = 3y - 15

x - 3y = -15+5

x - 3y = -10  ---------(1)

Ten years later, a shall be twice as old as b  

i.e. age of a will be x + 10 and age of b will  be 2(y+10)

x + 10 = 2 (y + 10)

x + 10 = 2y + 20

x - 2y = 20-10

x - 2y = 10  ---------(2)

By elimination method, we get

x - 3y = -10  

x - 2y = 10  

 - y = -20

y = 20 i.e. present age of b

Substituting y = 20 in equation 1, we get

x - 3y = -10    

x - 3(20) = -10

x - 60 = -10

x = -10 + 60

x = 50 i.e. present age of a.