Question

the sum of the ages of A and B is 29 years . after 8 years A will be twice as old as B ,find their present ages​

Answer 1

Answer:

Given:

• Sum of ages = 29
• After 8 years , A is twice old as B

Solution:

Let :

• Age of A = x years
• Age of B = y years

Now forming first equation:

x + y = 29⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀-(i)

Now given second equation, after 8 years:

• Age of A = 8 + x years
• Age of B = 8 + y years

ATQ :

Age of A = 2 × Age of B

(8 + x) = 2(8 + y)

8 + x = 16 + 2y

x - 2y = 8⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀-(ii)

Subtracting (i) , (ii) :

x + y - (x - 2y) = 29 - 8

x + y - x + 2y = 21

3y = 21

y = 7

y = 7 x = 29 - y = 29 - 7 = 22

Hence age of A is 22 years and age of B is 7 years

Answer 2

TO FIND:

• Present ages of A and B .

ANSWER:

Given:

• Sum of ages of A and B is 29 years .
• After 8 years A will be twice as old as B.

How to solve?

• We will first consider ages of A and B as variables . Then according to the two statements given we will frame two equⁿs .Then by solving that pair of equⁿs we will find the ages of A and B .

Let us take the

1. Age of A as x.
2. Age of B as y.

$\underline{\red{\bf{\leadsto STATEMENT\:\:1:}}}$

• Sum of ages of A and B is 29 .

Atq , $\sf{x+y=29}$ ...........(i)

$\underline{\red{\bf{\leadsto STATEMENT\:\:2:}}}$

• After eight years ages A will be twice as ild as B .

So , after 8 years , Age of A will be x + 8 and that of B will be y + 8.

Atq , $\sf{2(y+8) = x + 8}$

$\sf{\implies 2y + 16 = x + 8}$

$\sf{\implies 2y - x = 8 - 16}$

$\bf{\mapsto 2y - x = -8}$ ...........(ii)

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Let's add both equ ⁿ s .

$\sf{\implies (x+y)+(2y-x) = 29-8}$

$\sf{\implies 3y = 29-8}$

$\sf{\implies y=\dfrac{21}{3}}$

$\purple{\bf{\longmapsto y = 7}}$

Hence ,

• Age of x = 29-y = 29-7 = 22 years.
• Age of y = 7 years