Question

sum of the digit of a two digit number is 12 if the digit are reversed the new number formed is 36 less than the original number find the original number​

Answer 1

Answer:

84

Step-by-step explanation:

Let x be 10s place & y be units place of the original number. Original number is 10A+B

A+B=12 ----------(1)

AFTER REVERSING THE DIGITS,

10B+A=10A+B- 36  

9B-9A=-36

9(B-A)=-36

A-B=4 ----------(2)

From Eq 1 and 2 we get

A=8 AND B=4.

SO, THE ORIGINAL NO.= 10A+B

                                         =10*8+4=84

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Answer 2

$\bf{\huge{\underline{\boxed{\sf{\blue{Answer:}}}}}}$

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

• Sum of the digit of a two digit number is 12
• The digit are reversed the new number formed is 36 less than the original number.

$\bf{\underline{\sf{\red{To\:find:}}}}$

• The original number.

$\bf{\underline{\sf{\red{Solution:}}}}$

Let the digit in the tens place be x

Let the digit in the units place be y

Original number = 10x + y

$\bf{\underline{\sf{\pink{As\:per\:the\:first\:condition:}}}}$

• Sum of the digit of a two digit number is 12

Representing it mathematically we will get our first equation.

x + y = 12 ----> 1

$\bf{\underline{\sf{\pink{As\:per\:the\:second\:condition:}}}}$

• The digit are reversed the new number formed is 36 less than the original number

Original number = 10x + y

Reversed number = 10y + x

Representing the second condition mathematically.

=> 10x + y -36 = 10y + x

=> 10x - x = 10y - y + 36

=> 9x = 9y + 36

=> 9x - 9y = 36

=> 9 ( x - y) = 36

=> x - y = $\sf\frac{36}{9}$

=> x - y = 4 ----> 2

Solve equations 1 and 2 simultaneously by elimination method.

Add equation 2 to 1,

+ x + y = 12 -----> 1

+ x - y = 4 ) -----> 2

------------------------------

2x = 16

x = $\sf\frac{16}{2}$

x = 8

Substitute x = 8 in equation 1,

x + y = 12 ----> 1

8 + y = 12

y = 12 - 8

y = 4

Digit in tens place = x = 8

Digit in units place = y = 4

Original number = 10x + y

Original number = 10 × 8 + 4

Original number = 80 + 4 = 84