I am thinking of a two−digit number .If i write 3 to the left of my number and double this three digit number the result is 27 times my original number. what is my number ?


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Question Number 118825 by bramlexs22 last updated on 20/Oct/20

$I a m t h i n k i n g o f a t w o - d i g i t n u m b e r$ $. I f i w r i t e 3 t o t h e l e f t o f m y n u m b e r$ $a n d d o u b l e t h i s t h r e e d i g i t n u m b e r t h e$ $r e s u l t i s 27 t i m e s m y o r i g i n a l n u m b e r .$ $w h a t i s m y n u m b e r ?$
	Answered by benjo_mathlover last updated on 20/Oct/20

	$l e t o r i g i n a l y o u r n u m b e r i s A B$ $t h e n 2 \times 3 A B = 27 \times A B$ $\Rightarrow 2 (300 + 10 A + B) = 27 (10 A + B)$ $\Rightarrow 600 + 20 A + 2 B = 270 A + 27 B$ $\Rightarrow 600 = 250 A + 25 B$ $\Rightarrow 24 = 10 A + B . T h u s y o u r n u m b e r i s 24$
	Answered by MJS_new last updated on 20/Oct/20

	$2 \times (300 + x) = 27 x$ $600 = 25 x$ $x = 24$
	Commented by PRITHWISH SEN 2 last updated on 20/Oct/20

	$simple and beautiful$
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