Question

what number must be added to each of 4 10 12 and 24 so that the resulting numbers are in proportion?

Answer 1

Refer to the attachment

Answer 2

$Given \: numbers \: 4, 10, 12 \:and \:24$

$Let \: the \:number \: should \:be\: added \:to \\each \:number \:so \:that \:the \: resulting \\numbers \:are \: in \: proportion \:is \:\pink {x}$

$\implies (4+x) : (10+x) = (12 + x ) : ( 24 + x )$

$\pink {product \:of \: means = product \:of \:extremes}$

$\implies (10+x)(12+x) = (4+x)(24+x)$

$\implies 120 + 10x + 12x + x^{2} = 96+4x+24x+x^{2}$

$\implies 120 + 22x = 96 + 28x$

$\implies 120 - 96 = 28x - 22x$

$\implies 24 = 6x$

$\implies x = \frac{24}{6}$

$\implies x = 4$

Therefore.,

$\red { Required \: number \: should \:be \: added } \green { = 4 }$

•••♪