Question

Two numbers are in the ratio 3:5. If 5 is subtracted from each of the number
then the ratio becomes 1:2. Find the numbers.​

Answer 1

${\Large{\pink{\boxed{\purple{\boxed{\green{\boxed{\red{\bf \ Answer}}}}}}}}}$

$\Large{\blue{\tt{\underline{\underline{Given \ :-}}}}}$

${\sf{☞ \ Ratio \ of \ numbers \ = \ 3:5}}$

If 5 is subtracted,

${\sf{☞ \ New \ ratio \ = \ 1:2}}$

$\Large{\green{\tt{\underline{\underline{To \ find \ :-}}}}}$

${\sf{✿ \ Both \ the \ numbers }}$

$\Large{\orange{\tt{\underline{\underline{Solution \ :-}}}}}$

${\tt{✯ \ Let \ the \ number \ be \ 3x, \ 5x \ and \ 1x \ and \ 2x}}$

According to question

${\tt{❥ \ If \ 5 \ is \ substracted \ the \ number \ will }}\\ {\tt{ be \ 1x \ and \ 2x}}$

${\sf{\longmapsto{ \frac{3x \: - \: 5}{5x \: - \: 5} \: = \: \frac{1x}{2x} }}}$

Cross multiplying

${\sf{\longmapsto{(3x - 5) ( 2x) = (5x - 5)(1x)}}}$

${\sf{\longmapsto{6 {x}^{2} - 10x \: = 5 {x}^{2} - 5x}}}$

${\sf{\longmapsto{6 {x}^{2} - 5 {x}^{2} = 10x - 5x}}}$

${\sf{\longmapsto{ {x}^{2} = 5x}}}$

${\sf{\longmapsto{ \cancel \frac{ {x}^{2} }{x} = 5}}}$

${\sf{\longmapsto{x = 5}}}$

${\sf{Original \ numbers \ -}}$

${\sf{↣ \ 3x \ = \ 3×5 \ = \ 15}}$

${\sf{↣ \ 5x \ = \ 5×5 \ = \ 25}}$