Question

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Answer 1

Step-by-step explanation:

5years ago,

let the age of A be x

then the age of B be 3x

after 10year (from present)

age of A be (x+5+10)

= x+15

age of B be = (3x+5+10)

= 3x+15

a/q after 10year age of A be twice of B

so,

2(x+15)=3x+15

2x+30=3x+15

x=15

present age of A = (x+5)

= 20

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Answer 2

Question:

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.

Answer:

Present age of A is 50 years

$\rule{70mm}{2pt}$

Step-by-step explanation:

Given that Five years ago, A was thrice as old as B and ten years later, A shall be twice as old as B. We need to find out the present age of A and B.

Assumption: Let's say that the present age of A is 'x' years and of B is 'y' years.

$\underline{\underline{\green{\sf{As\:per\:given\: question:}}}}$

"Five years ago, A was thrice as old as B." (If we multiply the age of B with three then their ages will be equal.)

Five years ago:

• Age of A = (x - 5) years
• Age of B = (y - 5) years

$\implies\:\sf{(x-5)=3(y-5)}$

Solve the bracket on RHS, and then solve further

$\implies\:\sf{x-5=3y-15}$

$\implies\:\sf{x-3y=-15+5}$

$\implies\:\sf{x-3y=-10}$

$\implies\:\sf{x=3y-10\:-----(eq 1)}$

$\underline{\underline{\green{\sf{As\:per\:given\: question}}}}$

"Ten years later, A shall be twice as old as B." (If we multiply the age of B with two then their ages will be equal.)

Ten years later:

• Age of A = (x + 10) years
• Age of B = (y + 10) years

$\implies\:\sf{(x+10)=2(y+10)}$

$\implies\:\sf{x+10=2y+20}$

$\implies\:\sf{x=2y+10\:----(eq2)}$

On comparing (eq 1) and (eq 2) we get,

$\implies\:\sf{3y-10=2y+10}$

$\implies\:\sf{3y-2y=10+10}$

$\implies\:\red{\sf{y=20}}$

(Present age of B)

Substitute value of y in (eq 1)

$\implies\:\sf{x=3(20)-10}$

$\implies\:\sf{x=60-10}$

$\implies\:\red{\sf{x=50}}$

(Present age of A)

Therefore, the present age of A is 50 years.