Question

A number consists of two digits whose sum is 12.if 18 is added to the number,its digits gets reversed.the number is.

Answer 1

Answer:

The solution can be obtained by letting x be the 'tens digit', and y be the unit digit, so that the original number is 10x+y. Then 10x+y+18=10y+x, because the digits are reversed. This simplifies to 9x+18=9y, or x+2=y. Since the digits add up to 12, x+y=12.

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Answer 2

✬ Original Number = 57 ✬

Step-by-step explanation:

Given:

• A number consists of two digits.
• Sum of digits of the number is 12.
• After adding 18 to the number it's digits get reversed.

To Find:

• What is the original number ?

Solution: Let the tens place digit be x and ones place digit be y. Therefore,

➟ Original number = is 10x + y and

➟ x + y = 12

➟ x = 12 – y.......(1)

Now after reversing the digits the new number formed is

➟ Reversed number = 10y + x

A/q

• After adding 18 to number the digits gets reversed.

$\implies{\rm }$ 10x + y + 18 = 10y + x

$\implies{\rm }$ 10x – x + 18 = 10y – y

$\implies{\rm }$ 9x + 18 = 9y

$\implies{\rm }$ 9(12 – y) + 18 = 9y

$\implies{\rm }$ 108 – 9y + 18 = 9y

$\implies{\rm }$ 126 = 9y + 9y

$\implies{\rm }$ 126 = 18y

$\implies{\rm }$ 126/18 = y

$\implies{\rm }$ 7 = y

So, The digits of number are

➯ One's place digit is y = 7

➯ Tens place digit is x = 12 – y

=> 12 – 7 = 5

Hence, the number is 10x + y

=> 10(5) + 7

=> 57