Question

Two numbers are in the ratio 2:3. If 9 is added to
each they will be in the ratio 3:4, the numbers are
( 12,
28 (2) 18,27 (3) 8, 12 (4) 10, 15​

Answer 1

$\Large{\underline{\underline{\mathfrak{\bf{Solution}}}}}$

$\Large{\underline{\mathfrak{\bf{Given}}}}$

• Two numbers are in the ratio 2:3
• If 9 is added to each they will be in the ratio 3:4

$\Large{\underline{\underline{\mathfrak{\bf{Explanation}}}}}$

Let,

• First Number = x
• Second Number = y

A/C to question,

==> x : y = 2 :3

==> x/y = 2/3

==> 3x - 2y = 0 -------------(1)

Again,

==> (x+9) : (y+9) = 3:4

==> (x+9)/(y+9) = 3/4

==> 4x - 3y = 27 - 36

==> 4x - 3y = - 9------------(2)

Multiply by 4 in equ(1) & 3 in equ(2)

• 12x - 8y = 0
• 12x - 9y = -27

________________Sub. it's

==> -8y + 9y = 27

==> y = 27

keep value of y in equ(1)

==> 3x - 2*27 = 0

==> 3x = 54

==> x = 54/3

==> x = 18

$\Large{\underline{\underline{\mathfrak{\bf{Hence}}}}}$

• First Number be = 18
• Second Number be = 27

_________________

Answer 2

Answer:

(2) 18,27

The numbers are

First number = 18

Second number = 27

Step-by-step explanation:

Given:

• Two numbers are in the ratio 2:3

• If 9 is added to each they will be in the ratio = 3:4

Find :

• The two numbers

Solution :

Let,

First number = 2x

Second number = 3x

9 is added to each number

So,

First number = 2x + 9

Second number = 3x + 9

They will be in the ratio = 3:4

According to question :

⇒ $\frac{2x + 9}{3x + 9} \: = \: \frac{3}{4}$

⇒ 4 (2x + 9) = 3 (3x + 9)

⇒ 8x + 36 = 9x + 27

⇒ 8x - 9x = 27 - 36

⇒ - 1x = - 9

⇒ 1x = 9

⇒ x = 9

★ First number = 2x

⇒ 2 (9)

⇒ 2 × 9

⇒ 18

★ Second number = 3x

⇒ 3 (9)

⇒ 3 × 9

⇒ 27

Therefore,

First number = 18

Second number = 27