a number of two digits has the sum of its digits as 7 when 9 is subtra

1.	a number of two digits has the sum of its digits as 7 when 9 is subtracted from the number, digits are reversed.the number is
Answer» Solving : LET digits at tens place be = x Digits at ONES place = y $\\ \large \sf \therefore \: number = 10x + y \\ \\ \large \sf \mapsto \: reversed \: \: number = 10y + x \\ \\ \large \star \underline{ \underline{ \sf \: according \: \: to \: \: question : }} \\ \\ \large \sf \: x + y = 7 \longrightarrow(i)\\ \\ \large \tt : \implies \: 10x + y - 9 = 10y + x \\ \\ \large \tt : \implies \: 10x - x + y - 10y = 9\\ \\ \large \tt : \implies \: 9x - 9y = 9 \sf \longrightarrow(ii) \\ \\$ $\large \rm \mapsto \underline{ \underline{ \rm \: by \: \: elimination \: \: method : }} \\ \\ \large \sf \: 9x - 9y = 9 \\ \\ \large \sf : \implies \: 9(x + y = 7) \\ \\ \large \sf : \implies \: 9x + 9y = 63\\ \\ \large \rm \: adding \: \: equations : \\ \\ \\ \large \sf : \implies \: 9x + \cancel{9y} = 63\\ \large \sf + \: \: \: 9x \: \cancel{- 9y} = 9 \\ \\ \\ \large \sf : \implies \: 18x = 72\\ \\ \\ \large \sf : \implies \: x = \frac{72}{18} \\ \\ \large \boxed{ \sf \therefore \: x = 4}\\ \\$ $\large \sf \: x + y = 7 \\ \\ \large \implies\sf \: 4 + y = 7 \\ \\ \implies\large \sf \: y = 7 - 4\\ \\ \large \boxed{ \sf \therefore \: y = 3}\\ \\$ $\large \sf number = 10x + y \\ \\ \large \sf \implies \: 10(4) + 3 \\ \\ \large \sf \: = \: 40 + 3$ Number = 43

a number of two digits has the sum of its digits as 7 when 9 is subtracted from the number, digits are reversed.the number is

Answer»

Solving :

LET digits at tens place be = x

Digits at ONES place = y

$\\ \large \sf \therefore \: number = 10x + y \\ \\ \large \sf \mapsto \: reversed \: \: number = 10y + x \\ \\ \large \star \underline{ \underline{ \sf \: according \: \: to \: \: question : }} \\ \\ \large \sf \: x + y = 7 \longrightarrow(i)\\ \\ \large \tt : \implies \: 10x + y - 9 = 10y + x \\ \\ \large \tt : \implies \: 10x - x + y - 10y = 9\\ \\ \large \tt : \implies \: 9x - 9y = 9 \sf \longrightarrow(ii) \\ \\$

$\large \rm \mapsto \underline{ \underline{ \rm \: by \: \: elimination \: \: method : }} \\ \\ \large \sf \: 9x - 9y = 9 \\ \\ \large \sf : \implies \: 9(x + y = 7) \\ \\ \large \sf : \implies \: 9x + 9y = 63\\ \\ \large \rm \: adding \: \: equations : \\ \\ \\ \large \sf : \implies \: 9x + \cancel{9y} = 63\\ \large \sf + \: \: \: 9x \: \cancel{- 9y} = 9 \\ \\ \\ \large \sf : \implies \: 18x = 72\\ \\ \\ \large \sf : \implies \: x = \frac{72}{18} \\ \\ \large \boxed{ \sf \therefore \: x = 4}\\ \\$

$\large \sf \: x + y = 7 \\ \\ \large \implies\sf \: 4 + y = 7 \\ \\ \implies\large \sf \: y = 7 - 4\\ \\ \large \boxed{ \sf \therefore \: y = 3}\\ \\$

$\large \sf number = 10x + y \\ \\ \large \sf \implies \: 10(4) + 3 \\ \\ \large \sf \: = \: 40 + 3$

Number = 43