Question

the sum of 2 digit number and number obtained by reversing the order of its digit is 165. if differ by 3 find the nummber

Answer 1

EXPLANATION.

• GIVEN

Sum of 2 digit number and the number

obtaining by reversing the order of its

digit = 165.

it is differ by = 3

To find the number.

According to the question,

Let the tens place be = x

Let the unit place be = y

original number = 10x + y

reversing number = 10y + x

Case = 1

Sum of 2 digit number and the number

obtaining by reversing the order of its

digit = 165.

=> 10x + y + ( 10y + x) = 165

=> 11x + 11y = 165

=> x + y = 15 ........ (1)

Case = 2

it is differ by = 3

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

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

=> 2x = 18

=> x = 9

put the value of x = 9 in equation (1)

we get,

=> 9 + y = 15

=> y = 6

Therefore,

Number = 10x + y = 10(9) + 6 = 96

original number = 96

Answer 2

Step-by-step explanation:

$\bf{\underline{\underline\red{Given:-}}}$

• The sum of a two digit number and number obtained by reversing the digits is 165.

• The difference of the digits = 3

$\bf{\underline{\underline\blue{To\:Find:-}}}$

• The number.

$\bf{\underline{\underline\green{Solution:-}}}$

Let the ones digit of the number be y

The tens digit of the number = x

The original number = 10x + y

The reversed number = 10y + x

According to the 1st condition

$\longrightarrow \rm(10x + y) + (10y + x) = 165$

$\longrightarrow \rm10x + y+ 10y + x = 165$

$\longrightarrow \rm11x + 11y= 165$

Dividing the whole equation by 11

$\longrightarrow \rm \dfrac{11x}{11} + \dfrac{ 11y}{11}= \dfrac{165}{11}$

$\longrightarrow \rm x + y= 15.....(i)$

According to the 2nd condition :-

The digits differ by 3

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

Adding equation (i) and (ii)

$\rm x \: + \not y = 15$

$\rm x \: - \not y = 3$

______________

$\rm \longrightarrow 2x = 18$

$\rm \longrightarrow x = \dfrac{18}{2}$

$\rm \longrightarrow x = 9$

Substituting x = 9 in equation (ii)

$\rm\longrightarrow x - y = 3$

$\rm\longrightarrow 9 - y = 3$

$\rm\longrightarrow y =9- 3$

$\rm\longrightarrow y =6$

Now:-

Substitute x = 9 and y = 6 in 10x + y

= 10(x) + y

= 10(9) + 6

= 96

$\underline{\boxed{\rm\purple{\therefore The \: number =96}}}$