Question

Two numbers are in the ratio of 2:3 if 4 be subtracted from each, they are in the ratio 3:5. Identify the numbers

Answer 1

$\sf{\bold{\green{\underline{\underline{Given}}}}}$

• Numbers are in the ratio = 2:3
• when 4 is subtracted from each it become = 3 : 5

______________________

$\sf{\bold{\green{\underline{\underline{To\:Find}}}}}$

• Correct numbers = ??

______________________

$\sf{\bold{\green{\underline{\underline{Solution}}}}}$

• let the number be 2x and 3x

⠀⠀⠀⠀

ATQ :- when 4 is subtracted from both it becomes 3 : 5

⠀⠀⠀⠀

$\sf: \implies{\bold{ \dfrac{2x - 4}{ 3x - 4} = \dfrac{3}{5}}}$

⠀⠀⠀⠀

$\sf: \implies{\bold{ 5 ( 2x - 4) = 3 ( 3x - 4)}}$

⠀⠀⠀⠀

$\sf: \implies{\bold{ 10x - 20 = 9x - 12}}$

⠀⠀

$\sf: \implies{\bold{ 10x - 9x = 20 - 12}}$

⠀⠀⠀⠀

$\sf: \implies{\bold{ x = 8}}$

⠀⠀⠀⠀

$\sf{\red{\boxed{\bold{x = 8}}}}$

⠀⠀

• Putting value of x in the numbers

⠀⠀⠀⠀

$\sf: \implies{\bold{ 2x }}$

⠀⠀⠀⠀

$\sf: \implies{\bold{ 2 \times 8}}$

⠀⠀⠀⠀

$\sf: \implies{\bold{ 16 }}$

⠀⠀⠀⠀

$\sf{\orange{\boxed{\bold{First\: number = 16 }}}}$

⠀⠀⠀⠀

$\sf: \implies{\bold{ 3x }}$

⠀⠀⠀⠀

$\sf: \implies{\bold{ 3 \times 8}}$

⠀⠀⠀⠀

$\sf: \implies{\bold{ 24 }}$

⠀⠀⠀⠀

$\sf{\orange{\boxed{\bold{Second\: number = 24 }}}}$

______________________

$\sf{\bold{\green{\underline{\underline{Answer}}}}}$

• Required numbers are 16 and 24

Answer 2

Answer:

Numbers are in the ratio = 2:3

when 4 is subtracted from each it become = 3 : 5

______________________

\sf{\bold{\green{\underline{\underline{To\:Find}}}}}

ToFind

Correct numbers = ??

______________________

\sf{\bold{\green{\underline{\underline{Solution}}}}}

Solution

let the number be 2x and 3x

⠀⠀⠀⠀

ATQ :- when 4 is subtracted from both it becomes 3 : 5

⠀⠀⠀⠀

\sf: \implies{\bold{ \dfrac{2x - 4}{ 3x - 4} = \dfrac{3}{5}}}:⟹

3x−4

2x−4

=

5

3

⠀⠀⠀⠀

\sf: \implies{\bold{ 5 ( 2x - 4) = 3 ( 3x - 4)}}:⟹5(2x−4)=3(3x−4)

⠀⠀⠀⠀

\sf: \implies{\bold{ 10x - 20 = 9x - 12}}:⟹10x−20=9x−12

⠀⠀

\sf: \implies{\bold{ 10x - 9x = 20 - 12}}:⟹10x−9x=20−12

⠀⠀⠀⠀

\sf: \implies{\bold{ x = 8}}:⟹x=8

⠀⠀⠀⠀

\sf{\red{\boxed{\bold{x = 8}}}}

x=8

⠀⠀

Putting value of x in the numbers

⠀⠀⠀⠀

\sf: \implies{\bold{ 2x }}:⟹2x

⠀⠀⠀⠀

\sf: \implies{\bold{ 2 \times 8}}:⟹2×8

⠀⠀⠀⠀

\sf: \implies{\bold{ 16 }}:⟹16

⠀⠀⠀⠀

\sf{\orange{\boxed{\bold{First\: number = 16 }}}}

Firstnumber=16

⠀⠀⠀⠀

\sf: \implies{\bold{ 3x }}:⟹3x

⠀⠀⠀⠀

\sf: \implies{\bold{ 3 \times 8}}:⟹3×8

⠀⠀⠀⠀

\sf: \implies{\bold{ 24 }}:⟹24

⠀⠀⠀⠀

\sf{\orange{\boxed{\bold{Second\: number = 24 }}}}

Secondnumber=24

______________________

\sf{\bold{\green{\underline{\underline{Answer}}}}}

Answer

Required numbers are 16 and 24