Question

A 2-digit number has 5 in the ones place. When 27 is added to the number, the digits are reversed. Find the number.

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Answer 1

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GiveN:

• A 2-digit number has 5 in the ones place.
• When 27 is added to the number, the digits are reversed.

To FinD:

• The two-digit number?

Step-by-Step Explanation:

Let the digits of the number be x and y.

Then the number will be 10x + y.

After reversing it will be 10y + x.

According to question,

⇒ Original number + 27 = Reversed number.

Now plug the values the given values of original number and the reversed number.

⇒ 10x + y + 27 = 10y + x

⇒ 10x - x + y - 10y + 27 = 0

⇒ 9x - 9y + 27 = 0

⇒ x - y + 3 = 0

As given in the question, the ones place of original no. is 5. Then, y = 5. Putting the value of y in the equation:

⇒ x - 5 + 3 = 0

⇒ x - 2 = 0

⇒ x = 2

Then the number will be:

⇒ 10(2) + 5 = 25 (Answer)

Answer 2

♣ Qᴜᴇꜱᴛɪᴏɴ :

• A 2-digit number has 5 in the ones place. When 27 is added to the number, the digits are reversed. Find the number

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♣ ᴀɴꜱᴡᴇʀ :

Required number = 25

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♣ ᴄᴀʟᴄᴜʟᴀᴛɪᴏɴꜱ :

As mentioned it is a 2 digit number, our answer should have 2 digits and also 5 is there in one place

Let x be a number in unknown digit of the required number

If x is in one's digit place , it value would be 1x, but it is in ten's digit place, so it's value is 10x

Actual number = 10x +5

Actual number + 27 = Number which is reversed

⇒ 10x + 5 + 27 = 10 × 5 + x

⇒ 10x + 32 = 50 + x

Subtract x from both sides

⇒ 10x + 32 - x = 50 + x - x

⇒ 9x + 32 = 50

Subtract 32 from both sides

⇒ 9x + 32 - 32 = 50 - 32

⇒ 9x = 18

Divide both sides by 9

⇒ 9x/9 = 18/9

⇒ x = 2

Actual number

= 10x + 5

= 10 × 2 + 5

= 20 + 5

= 25