Question

(4 m) 1. A positive number is 5 times another number. If 21 is added to both the numbers, then one of the new number becomes twice the other new number. What are the numbers? 2. Three conser​

Answer 1

Given : A positive number is 5 times another number & If 21 is added to both the numbers, then one of the new number becomes twice the other new number.

Need To Find : The numbers ?

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❍ Let's say , that the Other number be x and Positive number be 5x ,i.e. Positive number is 5 times another number.

$\\\dag \:\:\underline {\pmb {\frak{ According \:To\:The\:Given \:Question \::\:}}}$

⠀⠀▪︎⠀If 21 is added to both the numbers, then one of the new number becomes twice the other new number.

$\\\\:\implies \sf 2\:\;\Big\{ Other\:_{\:(No.)}\:+\:21\:\Big\}\:=\:\Big\{ Positive \:_{\:(No.)\:} \:+\:21 \:\Big\}\:$

$:\implies \sf 2\Big\{ x\:+\:21\:\Big\}\:=\:\Big\{ 5x \:+\:21 \:\Big\}\:$

$:\implies \sf \Big\{ 2x\:+\:42\:\Big\}\:=\:\Big\{ 5x \:+\:21 \:\Big\}\:$

$:\implies \sf 2x\:+\:42\:=\: 5x \:+\:21 \:$

$:\implies \sf 2x\:-\:5x\:=\: 21 \:-\:42 \:$

$:\implies \sf -\:3x\:=\: - 21 \:$

$:\implies \sf \:3x\:=\: 21 \:\qquad \Bigg \lgroup \:Eliminating \:\pmb{\sf - ve}\:sign\:\Bigg\rgroup$

$:\implies \sf \:x\:=\: \cancel{\dfrac{21}{3}} \:$

$:\implies \pmb {\underline {\boxed {\purple {\:\frak{ \:x\:\:=\:7\:}}}}}\:\bigstar \:$

Therefore,

• Positive Number , 5x = 5(7) = 35 &
• Other Number, x = 7

$\\\:\:\:\therefore \:\underline {\:\sf Hence, \:The \:numbers \:are\:\pmb{\sf 7\:\&\:35\:}\:.\:}$