a-two-digit-number-is-3-more-than-4-times-the-sum-of-its-digits-if-18-is-added-to-this-number-the-sum-is-equal-to-number-obtained-by-interchanging-the-digits-find-the-number-

Question Number 26156 by bbbbbb last updated on 21/Dec/17

a t w o d i g i t n u m b e r i s 3 m o r e t h a n

4 t i m e s t h e s u m o f i t s d i g i t s . i f

18 i s a d d e d t o t h i s n u m b e r . t h e

s u m i s e q u a l t o n u m b e r o b t a i n e d

b y i n t e r c h a n g i n g t h e d i g i t s . f i n d t h e n u m b e r

Answered by mrW1 last updated on 22/Dec/17

{l e t}^{'} s s a y t h e n u m b e r i s a b .

10 a + b = 4 (a + b) + 3 \dots (i)

10 a + b + 18 = 10 b + a \dots (i i)

(i) \Rightarrow 2 a - b = 1

(i i) \Rightarrow a - b = - 2

\Rightarrow a = 3

\Rightarrow b = 5

T h e n u m b e r i s 35 .

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