Question

The sum of the digits of a 2- digits number is 6 . on reversing its digits the new obtained . Is 45 more than the original number. Find the number​

Answer 1

Correct Question

The sum of the digits of a 2- digits number is 9. on reversing its digits the new obtained which is 45 more than the original number.

Find out

Find the number

Solution

★ Let the tens digit be x and ones digit be y

• Original number = (10x + y)

*According to the given condition*

✞Sum of the digits of a 2 - digits number is 6

• x + y = 9
• y + x = 9 ----(i)

✞On reversing its digits the new obtained which is 45 more than the original number.

• Reversed number = (10y + x)

➟ 10y + x = 10x + y + 45

➟ 10y - y + x - 10x = 45

➟ 9y - 9x = 45

➟ 9(y - x) = 45

➟ y - x = 5 ----(ii)

Add both the equations

➟ (y + x) + (y - x) = 9 + 5

➟ y + x + y - x = 14

➟ 2y = 14

➟ y = 14/2

➟ y = 7

Putting the value of y in eqⁿ (ii)

➟ y - x = 5

➟ 7 - x = 5

➟ x = 7 - 5

➟ x = 2

Hence,

• Original number = (10x + y)= 27
• Reversed number = (10y + x)= 72

$\rule{200}3$