Question

A number consists of two digit whose sum is 9. If 9 is subtracted from the number the digits interchange their places. Find the number.

a-36
b-54
c-45
d-63

Answer 1

$\huge{\underline{\purple{\rm{Solution:}}}}$

$\large{\underline{\red{\rm{Given:}}}}$

• A number consists of two digit whose sum is 9. If 9 is subtracted from the number the digits interchange their places

$\large{\underline{\green{\rm{Let:}}}}$

• $\sf{The\: ones\: digit=x}$
• $\sf{The\: tens\: digit=y}$
• $\sf{The\: Number=10y+x}$

$\small{\underline{\purple{\rm{As\:per\:the\: above\: information:}}}}$

$\sf{The\:sum\:of\:two\: digits=9}$

$\sf{\implies x+y=9}$

$\sf\green{\implies x+y=9-----(i)}$

$\sf{\implies If\:9\:is\: subtracted\: from\:the\: Number\:the\: digits\:are\: reversed\:in\: it's\: place}$

$\sf{\implies (10y+x)-9=10x+y}$

$\sf{\implies 10x-x+y-10y=-9}$

$\sf{\implies 9x-9y=-9}$

$\sf{\implies Dividing\:by\:9\:on\:both\: sides}$

$\sf\green{\implies x-y=-1-----(ii)}$

$\sf{\implies Solving\: equation\:1\:and\:2\: here,}$

$\sf{\implies x+y=9}$

$\sf{\implies x-y=-1}$

$\sf{\implies Adding\: equation\:here\:we\:get}$

$\sf{\implies \cancel{2}x=\cancel{8}}$

$\sf{\implies x=4}$

$\sf{\implies Now,\: putting\:the\: value\:of\:x=4\:in\:eq\:1}$

$\sf{\implies 4+y=9}$

$\sf{\implies y=9-4}$

$\sf{\implies y=5}$

hence,

$\sf\green{\implies The\: number=10y+x=10*5+4=54}$

Answer 2

Answer:

x+y =9

10x+y -9 = 10y+x

9x-9=9y

x-y=1

2x=10

x=5

y =4

the number is 54