Question

Two numbers in the ratio 2 : 3 If 9 is added to each, they will be in the ratio 3:4
the numbers are.
(1) 12,28 (2) 18, 27
(3) 8, 12 (4) 10, 15​

Answer 1

Required Answer:-

Given Statements:

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

To Find:

• The numbers.

Solution:

→ Let the numbers be 2x and 3x.

Therefore, on adding 9 to each values, we get,

→ First number = 2x + 9

→ Second number = 3x + 9

According to the given condition,

→ (2x + 9)/(3x + 9) = 3/4

On cross-multiplying, we get,

→ 4(2x + 9) = 3(3x + 9)

→ 8x + 36 = 9x + 27

→ 9x - 8x = 36 - 27

→ x = 9

Therefore,

→ First number = 2 × 9 = 18

→ Second number = 3 × 9 = 27

→ So, the numbers are 18 and 27.

Answer:

• The numbers are 18 and 27.

•••♪

Answer 2

Given : Two numbers in the ratio 2 : 3 If 9 is added to each, they will be in the ratio 3:4 .

Need To Find : The numbers .

⠀⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━⠀

❍ Let's consider the two number be 2x and 3x .

Given that,

⠀⠀⠀⠀⠀⠀⠀⠀If 9 is added to each, they will be in the ratio 3:4 .

Then ,

⠀⠀⠀⠀⠀ $\sf{\implies \: Formed\: Equation: \:\dfrac{2x + 9 }{3x + 9} = \dfrac{3}{4}}$

⠀⠀⠀⠀⠀Now Solving the Formed Equation for the value of x :

⠀⠀⠀⠀⠀ $\sf{\implies \: Formed\: Equation: \:\dfrac{2x + 9 }{3x + 9} = \dfrac{3}{4}}$

⠀⠀⠀⠀⠀ $\sf{\implies \: \:\dfrac{2x + 9 }{3x + 9} = \dfrac{3}{4}}$

By Cross Multiplication :

⠀⠀⠀⠀⠀ $\sf{\implies \: \:\dfrac{2x + 9 }{3x + 9} = \dfrac{3}{4}}$

⠀⠀⠀⠀⠀ $\sf{\implies \: \:4(2x + 9 )= 3(3x + 9) }$

⠀⠀⠀⠀⠀ $\sf{\implies \: \:8x + 36 = 9x + 27 }$

⠀⠀⠀⠀⠀ $\sf{\implies \: \: 36-27 = 9x - 8x }$

⠀⠀⠀⠀⠀ $\sf{\implies \: \: 36-27 = x }$

⠀⠀⠀⠀⠀$\underline {\boxed{\pink{ \mathrm {  x = 9\: }}}}\:\bf{\bigstar}$

Therefore,

• First Number = 2x = 2 × 9 = 18 .

• Second Number = 3x = 3 × 9 = 27 .

Therefore,

⠀⠀⠀⠀⠀$\therefore {\underline{ \mathrm {  Hence,\:The\:two\:numbers\:are\:18\:and\:27\:}}}$

⠀⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━⠀

$\large {\boxed {\sf{\mid{\overline {\underline {\bigstar Verification \:}}}\mid}}}$

As , We have ,

⠀⠀⠀⠀⠀ $\sf{\implies \: Formed\: Equation: \:\dfrac{2x + 9 }{3x + 9} = \dfrac{3}{4}}$

Here :

⠀⠀⠀⠀⠀ $\sf{\implies \: \: x = 9 }$

⠀⠀⠀⠀⠀⠀$\underline {\frak{\star\:Now \: By \: Substituting \: the \: x = 9\: in\:Formed \:Equation \::}}$

⠀⠀⠀⠀⠀ $\sf{\implies \: \:\dfrac{2\times 9 + 9 }{3\times 9 + 9} = \dfrac{3}{4}}$

⠀⠀⠀⠀⠀ $\sf{\implies \: \:\dfrac{18 + 9 }{27 + 9} = \dfrac{3}{4}}$

⠀⠀⠀⠀⠀ $\sf{\implies \: \:\dfrac{27 }{36} = \dfrac{3}{4}}$

⠀⠀⠀⠀⠀ $\sf{\implies \: \:\dfrac{3 }{4} = \dfrac{3}{4}}$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀$\therefore \bf{\underline { Hence,\:Verified \:}}$

⠀⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━⠀

⠀⠀⠀⠀⠀