Question

The sum of the digits of a two digit number is 12 .If the new number formed by reversing the digits is greater than the original number by 54, find the original number.​

Answer 1

Required Answer:-

Given:

• The sum of the digits of a two digit number is 12.
• The new number formed by reversing the digits is greater than the original number by 54.

To find:

• The number.

Solution:

Let the unit digit of the number is y and the tens digit of the number be x.

Therefore,

➡ x + y = 12 ......(i)

➡ Number = 10x + y

➡ Reversed Number = 10y + x

According to the given condition,

➡ 10y + x - (10x + y) = 54

➡ 9y - 9x = 54

➡ 9(y - x) = 54

➡ y - x = 6 ........(ii)

Adding equations (i) and (ii), we get,

➡ 2y = 12 + 6

➡ 2y = 18

➡ y = 9

Hence,

x = 12 - y

= 12 - 9

= 3

Hence, the number is,

= 10 × 3 + 9

= 39

Answer:

• The number is 39.

Verification:

Let us verify our result.

Sum of the digits,

= 3 + 9

= 12 which is correct.

Reversed number = 93

93 - 39

= 54 which is also right.

Hence, 39 is the original number (Hence Verified)

Answer 2

$\huge{Question}$

The sum of the digits of a two digit number is 12 .If the new number formed by reversing the digits is greater than the original number by 54, find the original number.

$\huge{Solutions}$

Let the digit in ones place be x

So, the digit in tens place be 12 - x

Original no.

= 10(12 - x) + 1(x)

= 120 - 10x + x

= 120 - 9x

New no.

= 10(x) + 1(12 - x)

= 10x + 12 - x

= 9x + 12  [∵By reversing the digits]

According to Question,

New no. - Original no. = 54

(9x + 12) - (120 - 9x) = 54

⇒ 9x + 12 - 120 + 9x = 54

⇒ 18x - 108 = 54

⇒ 18x = 54 + 108

⇒ 18x = 162

⇒ x = 162 / 18

⇒ x = 9

Required Numbers -

Original no. = 120 - 9x = 120 - 9(9)

= 120 - 81 = 39

New no. = 93 [∵By reversing the digits]

Hence, the required number is either 39 or 93

Check -

(i)...According to Question,

The sum of the digits of the two-digit number is 12

The digits are 3 and 9

∴ Sum of digits = 3 + 9 = 12

Hence, the require numbers are correct

(ii)... According to Question,

The new number is greater than Original number by 54

New number = 93

Original number = 39

∴ Clearly, 39 < 93

∴ 93 - 39 = 54

Hence, it is proofed that the required numbers are correct