Question

In a two-digit number, the tens digit is 5 less than the units digit. The number itself is five more than three times the sum of its digits. What is the number?

Answer 1

Answer:

38

Step-by-step explanation:

Answer 2

Given:

In a two-digit number, the tens digit is 5 less than the units digit.

The number itself is five more than three times the sum of its digits.

To find:

The number.

Solution:

Let the two digit number is ab. So,

$ab=10a+b$

Tens digit is 5 less than the units digit.

$a=b-5$       ...(i)

The number itself is five more than three times the sum of its digits.

$10a+b=3(a+b)+5$

$10a+b=3a+3b+5$

$10a+b-3a-3b=5$

$7a-2b=5$          ...(ii)

Using (i) and (ii), we get

$7(b-5)-2b=5$

$7b-35-2b=5$

$5b=5+35$

$5b=40$

$b=8$

Putting b=8 in (i), we get

$a=8-5$

$a=3$

Therefore, the required number is 38.