Question

which number should be subtracted from 7 ,12 and 18 such that resultant numbers are in continued proportion

Answer 1

Please see the attachment

Answer 2

$Let \: \pink{x} \: be \: the \: number \: that \\should\:be\: subtracted \: from \: 7, 12 , 18 \: so \\that \: the \: numbers \: remain \: in \: continued\\proportion .$

$\blue { Numbers \: a,b \:and \: c \:are \:said }\\\blue { to \: be \: continued \:proportion }$

$\orange { b^{2} = ac}$

$Here, \frac{7-x}{12-x} = \frac{12-x}{18-x}$

$\implies (7-x)(18-x) = (12-x)^{2}$

$\implies 126 - 7x - 18x + x^{2} = 12^{2} + x^{2} - 24x$

$\implies 126 - 25x = 144 + - 24x$

$\implies 126 - 144 = 25x - 24x$

$\implies -18 = x$

Therefore.,

$\green {-18} \: should \:be \: subtracted \:from\\7,12, 18 \:so \:that \: the \: numbers \:remain \: in \\continued \: proportion.$

•••♪