Question

The sum of the digits of a two-digit number is. If the digits are reversed, the number is reduced by 27. Find the number.​

Answer 1

correct question.

The sum of the digit of a two digit number is 5.

if the digit are reversed,the number is reduced

by 27. find the number.

EXPLANATION.

Let the digit at unit place be = x

Let the digit of tens place be = y

according to the question,

sum of the digit of two digit number is =

x + y = 5 ....(1)

if the digit is reversed, the number is reduced

by 27

if digit are reversed = 10y + x

10y + x - (10x + y) = 27

10y + x - 10x - y = 27

9y - 9x = 27

y - x = 3 .....(2)

From equation (1) and (2) we get,

2y = 8

y = 4

put y = 4 in equation (1) we get,

x + 4 = 5

x = 1

Therefore,

Required number = 10y + x

10(4) + 1 = 41

Required number is = 41

Answer 2

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

• The sum of the digits of a two-digits is 5

• If the digits are reversed, the number is reduced by 27.

$\large \rm \blue { \underline{ \underline {To\:Find:-}}}$

• The number.

$\large \rm \green { \underline{ \underline {Solution:-}}}$

$\rm \: Let \: the \: units \: digit \: of \: the \: number \: be \: x$

$\rm \: and \: the \: tens \: digit \: of \: the \: number \: be \: y$

Therefore y + x= 5 ........ (i)

According to the question:-

$\rm \: Original \: number \: = 10y + x$

$\rm \: Reversed \: number \: = 10x + y$

According to Condition 2:-

Given, if the digits are reversed the number is reduced by 27

So:-

$\rightarrow \rm 10y + x - (10x + y) = 27$

$\rightarrow \rm 10y + x - 10x - y = 27$

$\rightarrow \rm 9y - 9x = 27$

Dividing the whole equation by 9

$\rightarrow \rm y - x = 3.....(ii)$

Adding equation (i) and (ii)

y + x = 5

y - x = 3
_________
$\rightarrow \rm 2y = 8$

$\rightarrow \rm y = \dfrac{8}{2}$

$\rightarrow \rm y = 4.......(iii)$

Substituting equation (iii) in (i)

$\rightarrow \rm y + x = 5$

$\rightarrow \rm 4 + x = 5$

$\rightarrow \rm x = 5 - 4$

$\rightarrow \rm x = 4$

Substituting values of x and y in in 10y + x

$\rightarrow \rm 10(4)+ 1$

$\rightarrow \rm 41$

$\large \boxed{\rm \purple{ \therefore The \: required \: number \: is \: 41} }$