Question

two numbers are in the ratio 6:8 if 10 is subtracted from each of the numbers , the new number are in the ratio 16 :32 ​

Answer 1

$\sf\red{\underline{\underline{Answer:}}}$

$\sf{Numbers \ are \ 15 \ and \ 20.}$

$\sf\orange{Given:}$

$\sf{\implies{Two \ numbers \ are \ in \ ratio \ of \ 6:8}}$

$\sf{\implies{If \ 10 \ is \ subtracted \ from \ each \ of}}$

$\sf{the \ numbers, \ the \ new \ numbers \ are }$

$\sf{in \ the \ ratio \ of \ 16:32}$

$\sf\pink{To \ find:}$

$\sf{The \ numbers.}$

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

$\sf{Let \ the \ common \ multiple \ be \ x.}$

$\sf{According \ to \ the \ first \ condition}$

$\sf{Numbers \ in \ ratio=\frac{6x}{8x}}$

$\sf{=\frac{3x}{4x}}$

$\sf{\therefore{Numbers \ are \ 3x \ and \ 4x}}$

$\sf{According \ to \ the \ second \ condition}$

$\sf{\frac{3x-10}{4x-10}=\frac{16}{32}}$

$\sf{\therefore{\frac{3x-10}{4x-10}=\frac{1}{2}}}$

$\sf{\therefore{2(3x-10)=4x-10}}$

$\sf{\therefore{6x-20=4x-10}}$

$\sf{\therefore{6x-4x=10}}$

$\sf{\therefore{2x=10}}$

$\sf{\therefore{x=\frac{10}{2}}}$

$\boxed{\sf{\therefore{x=5}}}$

$\sf{Numbers=3(5) \ and \ 4(5)}$

$\sf{\therefore{Numbers=15 \ and \ 20}}$

$\sf\purple{\tt{\therefore{Numbers \ are \ 15 \ and \ 20.}}}$

Answer 2

Hello,

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

➥Two no. are in ratio = 6:8

➥If we will subtract 10 from each no. then we will get new no. in the form of ratio = 16:32

$\large{\boxed{\underline{\bold{\red{\sf{Let\:Common\:Multiple\:be\:x}}}}}}$

━━━━━━━━━━━━━━━━━━━━

$\large{\underline{\underline{\bold{\blue{\sf{According\:to\:Question : -}}}}}}$

No in ratio = $\cancel\dfrac{6x}{8x}$

$\dfrac{3x}{4x}$

Hence,the no. are 3x and 4x

━━━━━━━━━━━━━━━━━━━━

$\dfrac{3x-19}{4x-10}=\cancel\dfrac{16}{32}$

$\dfrac{1}{2}$

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$2(3x-10)=4x-10$

$6x-20=4x-10$

$6x-4x=10$

$2x=10$

$x=\cancel\dfrac{10}{2}$

$x=5$

Numbers are 15 and 20