Question

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Answer 1

Question:

Five years ago,A's age was four times the age of B. 5 years hence, A's age will be twice of the age of B. Find their present ages.

Given:

• Five years ago, A's age was 4 times the age of B.

• .Five years hence A's age will be twice of the age of B.

To find:

• Age of A

• Age of B

Let :

• present age of A = x

• present age of B = y

Answer:

Five years ago:

• Age of A= x-5

• Age of B=y-5

As it's Given 5 years ago A's age was 4 times the age of B

.°. Equation formed as follows:

$\sf{}x - 5 = 4(y - 5)$

Now Let's solve this equation:

$: \implies\sf{}x - 5 = 4y - 20$

$: \implies \sf{}x - 4y = - 15$

$: \implies \sf{}y = \dfrac{ - 15 - x}{ - 4}$

$: \implies \sf{}y = \dfrac{ 15 + x}{ 4} \small{........................... \green{⓵}}$

Five years hence:

• Age of A= x+5

• Age of B = y+5

As it's given 5 years hence A's age will be twice of the age of B.

.°. Equation formed as follows:

$\sf{}x + 5 = 2(y + 5)$

$: \implies \sf{}x + 5 = 2y + 10$

$: \implies \sf{}x - 2y = 10 - 5$

$: \implies \sf{}x - 2y = 5\small{........................... \green{⓶}}$

Now put value of y in Equation 2

$: \implies\sf{}x - 2 [\dfrac{ 15 + x}{ 4}] = 5$

$: \implies\sf{}x - \dfrac{ 30+2 x}{ 4}= 5$

multiply each digit by 4

$: \implies \sf{}4x - (30 + 2x) = 20$

$: \implies\sf{}4x -30 - 2x = 20$

$: \implies\sf{}4x - 2x = 20 + 30$

$: \implies\sf{}2x = 50$

$: \implies\sf{}x = \dfrac{50}{2}$

$: \implies\sf{}x = \dfrac{ { \cancel{50}}^{ \: \: 25} }{ { \cancel2}^{ \: \: 1} }$

$: \implies \star \boxed{ \sf{}x = 25} \star$

we got value of x i.e.25

Put value of x in equation 1:

$: \implies \sf{}x - 2y = 5$

$: \implies \sf{}25 - 2y = 5$

$: \implies \sf{} - 2y = 5 - 25$

$: \implies \sf{} - 2y = - 20$

$: \implies \sf{} y = \dfrac{ - 20}{ - 2}$

$: \implies \sf{} y = \dfrac{ 20}{ 2}$

$: \implies \sf{} y = \dfrac{ { \cancel{20}}^{ \: 10} }{ { \cancel{2}}^{ \: 1} }$

$: \implies \star \boxed{ \sf{}y= 10} \star$

As we have supposed A's age as x

.°. A's age = 25

As we have supposed B's age as y

.°. B's age = 10

Now Let's Verify their ages:

Put age of A and B in Equation 1:

$\sf{}25 - 5 = 4(10 - 5)$

$: \implies \sf{}20= 40 - 20$

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

☆Hence Verified ☆

__________________________________________________

And all we are done! ✔

:D

Answer 2

Answer:

Let us consider B’s age = X

Then A’s age = 4X

Five years ago

⇒ A’s age = 4X + 5

⇒ B’s age = X + 5

Five years hence

⇒ A’s age = 4X + 5 + 5

⇒ A’s age = 4X + 10

⇒ B’s age = X + 5 + 5

⇒ B’s age = X + 10

From the given question

4X + 10 = 2(X + 10)

4X + 10 = 2X + 20

4X – 2X = 10

2X = 10

X = 5

A’s age = 4X + 5

A’s age = 25 years

B’s age = X + 5

B’s age = 10 years

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