Question

Sum of digits of a two digit numbers is 12
On interchanging their digits, new number
formed will be 54 more than original
number. Find original number.​

Answer 1

Step-by-step explanation:

Assumption: Let the two digit number be 10x + y.

x + y = 12 ______ equation i

10y + x = ( 10x + y ) + 54

=> x + 10y = 10x + y + 54

=> - 9x + 9y = 54

=> 9x - 9y = 54

=> 9 ( x - y ) = 54

=> x - y = 6 ________ equation ii

By elimination method :-

For eliminating y, eq i × 1 + eq ii × 1,

x + y = 12

+ x - y = 6

2x = 18

=> x = 9

Putting x = 9 in eq i,

x + y = 12

=> 9 + y = 12

=> y = 12 - 9

=> y = 3

Therefore, x = 9 and y = 3.

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Answer 2

Answer:

The Original Number is 39.

Step-by-step explanation:

Given :

Sum of the digits = 12

Number formed after reversing the digits = 54 more than the original number

To find :

The Original Number

Solution :

Original Number -

Let the Digits be -

• Units Place as x
• Tens Place as 10(12 - x)

$\longrightarrow$ 10(12 - x) + x

$\longrightarrow$ 120 - 10x + x

$\longrightarrow$ 120 - 9x ....... [Original Number]

$\rule{300}{1.5}$

Number with Reversed Digits -

Let the Digits be -

• Units Place as (12 - x)
• Tens Place as 10(x)

$\longrightarrow$ 10(x) + (12 - x)

$\longrightarrow$ 10x + 12 - x

$\longrightarrow$ 9x + 12 ....... [Number With Reversed Digits]

$\rule{300}{1.5}$

According to the Question -

Number formed after reversing the digits = 54 more than the original number

$\longrightarrow$ 9x + 12 = (120 - 9x) + 54

$\longrightarrow$ 9x + 12 = 174 - 9x

$\longrightarrow$ 9x + 9x = 174 - 12

$\longrightarrow$ 18x = 162

$\longrightarrow$ x = 162/18

$\longrightarrow$ x = 9

$\rule{300}{1.5}$

★ Original Number -

$\longrightarrow$ 120 - 9x

$\longrightarrow$ 120 - 9(9)

$\longrightarrow$ 120 - 81

$\longrightarrow$ 39

$\therefore$ The Original Number is 39.

$\rule{300}{1.5}$

Verification:

Original number = 39

Number With Reversed Digits = 93

$\longrightarrow$ 39 + 54 = 93

$\longrightarrow$ 93 = 93

$\longrightarrow$ LHS = RHS

$\therefore$ The Original Number is 39.