Question

A positive number is 5 time another number. If 21 is added to both the numbers, then one of the new numbers become twice of other new numbers. Find the original numbers.​

Answer 1

❍ Let's say, that the other number be x.

Given that,

• A positive number is five times the other Number.

➟ Postive no. = 5 × (Other no.)

➟ Positive number = 5x

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$\underline{\bigstar\:\boldsymbol{By \; given \: Condition\;:}}$⠀⠀

• And it is given that, If 21 is added to both the numbers, then one of the new number become twice of other new numbers.

⠀

✰ Adding 21 to both numbers —

• Other no. = (x + 21)
• Postive no. = (5x + 21)

⠀⠀⠀

Therefore,

⠀⠀⠀

$:\implies\sf 5x + 21 = 2(x + 21)\\\\\\:\implies\sf 5x + 21 = 2x + 42\\\\\\:\implies\sf 5x - 2x = 42 - 21\\\\\\:\implies\sf 3x = 21\\\\\\:\implies\sf x = \cancel\dfrac{21}{3}\\\\\\:\implies\underline{\boxed{\frak{\purple{x = 7}}}}\;\bigstar$

⠀⠀⠀

Hence,

• Other number, x = 7
• Postive number, 5x = 5(7) = 35

⠀⠀

$\therefore{\underline{\textsf{Hence, the original numbers are \textbf{7}\:\sf{and}\;\textbf{35}\: \sf{respectively.}}}}$⠀⠀⠀⠀⠀⠀

Answer 2

$\bf Given \:\:: \begin{cases}\sf A\: positive\: number\: is\: 5 \:time \:another\: number\:.\\\\ \qquad \bf AND \:, \:\\\\ \sf 21 \:is \:added \:to\: both\: the\: numbers,\: then\: one\: of \:the \:new\: numbers\:\\ \qquad \sf become\: twice \:of \:other\: new \:numbers\: .\end{cases}$

Exigency To Find : The Original number .

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⠀⠀❍ Let's Assume the other number be a .

⠀⠀Therefore,

⠀⠀⠀⠀ For positive umber , Given that ;

⠀⠀⠀⠀⠀⠀▪︎⠀⠀A positive number is 5 times another number.

$\qquad :\implies \sf Positive \:number \:\: \: 5 \times Other\;number \:$

$\qquad :\implies \sf Positive \:number \:\:= \: 5 \times a \:$

$\qquad :\implies \sf Positive \:number \:\:= \: 5a \:$

$\qquad \therefore \:\:\underline{\pmb{\pink{\: Positive \:number \:\:= \: 5a }} }\:\:\bigstar$

⠀⠀⠀⠀⠀⠀$\underline {\boldsymbol{\star\:According \:\: to \:\: Question \: \: \::}}$

⠀━━ If 21 is added to both the numbers, then one of the new numbers become twice of other new numbers.

$\qquad:\implies \sf 21 + Positive \:number \: = \: 2 \ ( \ Other\:number \:+ \:21 \ )$

$\qquad:\implies \sf 21 + 5a \: = \: 2 \ ( \ a \:+ \:21 \ )$

$\qquad:\implies \sf 21 + 5a \: = \: 2 a \:+ \:42$

$\qquad:\implies \sf 5a \: = \: 2 a \:+ \:42 \ - 21 \:$

$\qquad:\implies \sf 5a \: = \: 2 a \:+ \: 21 \:$

$\qquad:\implies \sf 5a - \:2a \: = \: \: 21 \:$

$\qquad:\implies \sf 3a \: = \: \: 21 \:$

$\qquad:\implies \sf a \: = \: \: \dfrac{21}{3} \:$

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

$\qquad:\implies \sf a \: = \: \: 7 \:$

$\qquad \therefore\:\: \underline{\pmb{\pink{\: a \: = \: \: 7 \: }} }\:\:\bigstar$

⠀⠀⠀⠀⠀⠀▪︎⠀⠀Here , a denotes Other number which is 7 .

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀AND ,

⠀⠀⠀⠀⠀⠀▪︎⠀⠀The Positive number is 5a = 5 × 7 = 35 .

⠀⠀⠀⠀⠀$\therefore {\underline{ \sf \:Hence, \:The \: \:numbers\:are\:\bf 7 \:\:\sf and \: \bf 35 \:\sf, \:respectively\: .}}$