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-

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