Question

A two digit number seven times the sum of its digits. The number formed by reversing the digit is 18 less than the given number. Find the given number.

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Answer 1

Answer:

42

Step-by-step explanation:

Let the unit digit be 'y' and ten's digit be 'x'. So, the number be 'xy'.

 We can write this as 10x + y,  in the same manner as 24 = 2(10) + 4 , 45 = 4(10) + 5 , etc.

Given,

        Number is 7 times the sum of digit

⇒ number = 7 * (sum of digits)

⇒ 10x + y = 7(x + y)

⇒ 3x = 6y

⇒ x = 2y           ...(1)

        The number formed by reversing the digits is 'yx' which can be written as 10y + x.

  Given, the reversed number is 18 less than the given number.

⇒ original number - 18 = reversed number

⇒ 10x + y - 18 = 10y + x

⇒ 9x - 9y = 18

⇒ x - y = 2

⇒ 2y - y = 2           [from (1),  x = 2y]

⇒ y = 2

   Substituting this in (1), we get

⇒ x = 2y = 2(2) = 4

Hence the required number is xy = 42.

Answer 2

Given : A two digit number seven times the sum of its digits. The number formed by reversing the digit is 18 less than the given number. Find the given number.

Need to Find : The given number

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★ Cᴏɴᴄᴇᴘᴛ :

According to the question, first we need to assume the unit's digit and ten's digit. After which we need to provide the suitable data present in the question and again reversing the ten's digit and unit's and putting the suitable data we can get the answer.

★ Sᴏʟᴜᴛɪᴏɴ :

Let us assume ten's digit be a and unit's digit be b

Hence, the number is ab

After which we can write it as 10a + b

Now, according to the question the two digit number is 7 times the sum of digits

So,

• 10a + b = 7(a + b)

• 10a + b = 7a + 7b

• 10a - 7a = 7b - b

• 3a = 6b

• a = 2b .... eq(1)

Now, again we need to reverse the digits

So, the reverse of 10a = 10b and reverse of b = a

Now, it's given that the number formed by reversing the digit is 18 less than the given number

Here the given number refers the original number

• 10a + b - 18 = 10b + a

Now, as we know that a = 2b from eq(1)

• 10(2b) + b - 18 = 10b + 2b

• 20b + b - 18 = 12b

• 21b - 12b = 18

• 9b = 18

• b = 2

From here we got b's value which is 2

Now, getting the value of a from eq(1)

• a = 2b

• a = 2(2)

• a = 4

For finding the given number we need to substitute the values in 10a + b

• 10a + b

Putting a = 4 and b = 2 we get

• 10(4) + 2

• 40 + 2

• 42

Tʜᴇ Nᴜᴍʙᴇʀ Is 42 Wʜɪᴄʜ ɪs Tʜᴇ Rᴇϙɪᴜʀᴇᴅ Aɴsᴡᴇʀ