Question

Ten years later, ‘A’ will be twice as old as 'B' and five years ago, 'A'
was 3 times as old as 'B'. What are their present ages?​

Answer 1

Step-by-step explanation:

Ten years later, ‘A’ will be twice as old as 'B' and five years ago, 'A'

was 3 times as old as 'B'. What are their present ages?

answer.

here.

Call A and B the 2 present ages.

Ten years from now, A is twice as old as B

(A + 10) = 2(B + 10)................ (1)

Five years ago, A was 3 times as old as B

(A - 5) = 3(B - 5) .....................(2).

Solve the system (1) and (2).

From (2) --> A = 3B - 15 + 5 = 3B - 10.

Replace this value of A into (1) -->

3B - 10 + 10 = 2B + 20

B = 20

Present age of B is20..

hope this will help you.

thank you

Answer 2

★ Given :

• Ten years later, ‘A’ will be twice as old as 'B'
• Five years ago, 'A' was 3 times as old as 'B'

★ To Find :

• Present age.

★ Solution :

Let the present age of A be x years.

Let the present age of B be y years.

★ Case 1 :

★Age ten years later :

• A's age : x + 10 years
• B's age : y + 10 years

$\longrightarrow$ $\mathtt{x+10\:=\:2(y+10)}$

$\longrightarrow$$\mathtt{x+10\:=\:2y\:+\:20}$

$\longrightarrow$ $\mathtt{x-2y\:=\:20\:-10}$

$\mathtt{x-2y=10}$ _____(1)

★ Case 2 :

★ Age five years ago :

• A's age : x - 5 years
• B's age : y - 5 years

$\longrightarrow$ $\mathtt{x-5\:=\:3(y-5)}$

$\longrightarrow$ $\mathtt{x-5=3y-15}$

$\longrightarrow$ $\mathtt{x-3y\:=\:-15+5}$

$\mathtt{x-3y=-10}$ _____(2)

★ Solving equations 1 and 2,

Subtract equation 2 from 1,

$\longrightarrow$ $\mathtt{x-3y-(x-2y)= -10-(+10)}$

$\longrightarrow$ $\mathtt{x-3y\:-x\:+\:2y\:=\:-10\:-10}$

$\longrightarrow$ $\mathtt{-3y+2y\:=\:-20}$

$\longrightarrow$ $\mathtt{-y\:=\:-20}$

$\longrightarrow$ $\mathtt{y=20}$

★ Substitute y = 20 in equation (1),

$\longrightarrow$ $\mathtt{x-2y\:=\:10}$

$\longrightarrow$ $\mathtt{x-2(20)\:=\:10}$

$\longrightarrow$ $\mathtt{x-40\:=\:10}$

$\longrightarrow$ $\mathtt{x=10+40}$

$\longrightarrow$ $\mathtt{x=50}$

$\large{\boxed{\sf{\red{Present\:age\:of\:A\:=\:x\:=\:50\:years}}}}$

$\large{\boxed{\sf{\red{Present\:age\:of\:B\:=\:y\:=\:20\:years}}}}$