Question

the unit digit of a two digit number is 3 and seven times the sum of the digit is the number itself. find the number ​

Answer 1

${\bold{\sf{\underline{Question \; is \; given}}}}$

The unit digit of a two digit number is 3 and seven times the sum of the digit is the number itself. Find the number.

${\bold{\sf{\underline{Given \; that}}}}$

✠ The unit digit of a two digit number is 3.

✠ Seven times the sum of the digit is the number itself.

${\bold{\sf{\underline{To \; find}}}}$

✠ The original number.

${\bold{\sf{\underline{Solution}}}}$

✠ The original number = 63.

${\bold{\sf{\underline{Understanding \; the \; question}}}}$

✠ This question says that there is a number whose unit digit of two digits is 3 and the tens place number is not given ; and it's 7 times the sum of the digit is the number itself. And at the end the question ask us to find the original number.

${\bold{\sf{\underline{Assumptions}}}}$

✠ Ten's digit / place of two digits number will be a.

${\bold{\sf{\underline{Procedure \: of \: question}}}}$

✠ To solve this question we have to use our taken assumption afterthat seeming the question ; we have to put the values. We get 6 as the value of a means as the ten's digit and we already know that unit digit is 3 hence, 63 is original number.

${\bold{\sf{\underline{Full \: solution}}}}$

• Ten's digit / place of two digits number will be a

• Therefore, the original number be 10a + 3

• Seven times the sum of the digit is the number itself

Now, coming to the question

➥ 7(a + 3) = 10a + 3

➥ 7a + 21 = 10a + 3

➥ 7a - 10a = 3 - 21

➥ -3a = -18

➥ a = -18 / -3

➥ a = 18 / 3

➥ a = 6

Henceforth,

↝ Ten's digit is 6

↝ Unit digit is 3

Therefore,

↝ Original number = 63

Answer 2

Answer:

The original number is 63.

Step-by-step explanation:

Given:

• Unit digit of a two digit number is 3.
• Seven times the sum of the digit is the number itself.

To find:

• Original number?

Solution:

☯ Let the ten's digit of a two digit number be x.

Therefore,

• Original number = (10x + 3)

Now,

★ According to the Question:

• 7 times the sum of the digit is the number itself.

⇒ 7(x + 3) = 10x + 3

⇒ 7x + 21 = 10x + 3

⇒ 10x - 7x = 21 - 3

⇒ 3x = 18

⇒ x = 18/3

⇒ x = 6

Therefore,

• Required number, (10x + 3) = 60 + 3 = 63

∴ Hence, the original number is 63.