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

Step-by-step explanation:

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.

Answer 2

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Let the present age 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) =>3x-y =10. - - - - - - - (1)

B's age 10 years hence = (x+10)years.

A's age 10 years hence = (y+10) years.

Therefore, (y+10)=2(x+10)=> 2x-y = - 10. ---------(2)

On subtracting (2)from (1),we get, x=20.

Putting x=20 in (1),we get

(3*20)-y =10 =>y=50.

Therefore, x =20 and y =50.

Hence, B's present age =20 years

And, A' s present age =50 years.