Question

a number has two digits whose sum is 7 if 27 is added to the number its digits gets interchanged find the number

Answer 1

the required number is 25

Answer 2

Answer:

Let the digits in the units place be x.

Then the digit in the ten's place = (7-x)

number = 10 × (7 - x) + x = 70 -10x + x = 70 - 9x

number with interchanged digits = 10 × x + (7 - x)

= 10x + 7- x = 9x + 7

Given:-

number + 27 = number with interchanged digits

70 - 9x + 27 = 9x +7

97 - 9x = 9x +7

18x = 90

$x \: \frac{90}{18} = 5 \\ \\ since \: x \: = 5 \: therefore \: 7 - x = 7 - 5 = 2$

Thus, thr digit in the unit place = 5 and the digit in the ten's palce = 2

✅ Hence the required number is 25.