Question

A number is divided into two parts such that one part is 10 more than the other. If the two
parts are in the ratio 5:3, find the number and the two parts.
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Answer 1

Step-by-step explanation:

$\bf\underline{\underline{\red{Given:-}}}$

• A number is divided into two parts such that one part is 10 more than the other.

• The two parts are in the ratio 5:3.

$\bf\underline{\underline{\blue{To\:Find:-}}}$

• The number

• The two parts of the number.

$\bf\underline{\underline{\green{Solution:-}}}$

$\sf Let \: one \: part \: of \: the\: number\: be \: x$

$\sf As,\: one\: part\: is\: 10 \:more\: than\: the\: other \:part$

$\sf The \: other \: part = x + 10$

$\sf Given, \: two\: parts\: are\: in\: the \: ratio\: 5 : 3$

$\sf So:-$

$\sf \implies\dfrac{x + 10}{x} = \dfrac{5}{3}$

$\underline{\sf By\: cross\: multiplication:-}$

$\sf \implies{3(x + 10)} = {5(x)}$

$\sf \implies3x + 30 = 5x$

$\sf \implies 30 = 5x - 3x$

$\sf \implies 30 = 2x$

$\sf \implies 2x = 30$

$\sf \implies x = \dfrac{30}{2}$

$\sf \implies x = 15$

$\sf One \: part \: of \: the\: number = x = 15$

$\sf The\: other\: part \: of \: the \: number = x + 10 = 15+ 10 = 25$

$\sf The\: number :-$

$\sf = x + x + 10$

$\sf = 15 + 25$

$\sf = 40$

$\underline{\boxed{\pink{\sf \therefore The \: number = 40}}}$

$\underline{\boxed{\purple{\sf \therefore The \: two\: parts\: of \: the\: number \: are \:15 \: and \:25}}}$