Question

The least number that must be subtracted from each of the numbers 14,17,34 and 42 so that, the remainders are in proportional is?​

Answer 1

$\red{\textbf{Answer :- 2}}$

Step-by-step explanation:

$To \: be \: in \: proportion,$

$we \: subtract  \: x \:  from \: each \: number$

$14−x:17−x$

$= 34−x:42−x$

$⇒ \Large\frac{14 -x }{17 - x} = \frac{34 - x}{42 - x}$

$⇒(14 - x )(42 - x) = (34 - x)(17 -x)$

$⇒ {x}^{2} - 56 + 588 = {x }^{2} - 51x + 578$

$⇒5x = 10$

$⇒x = \Large\frac{10}{5}$

$⇒x = 2$

so, number 2 is subtracted from each of the no.so that remainder are in proportion.