Question

his SIS
A number consists of two digits whose sum is 9. If 9 is subtracted from the number, its digits are
interchanged. Find the numbers.
it
She multiplies the result by 8. The result now​

Answer 1

Answer:

Let the digits at ones place be x

Then the digits at tens place=9-x     ......(sum of two digits is 9)

Therefore the number =10 (9-x)+x=90-10x+x=90-9x

Now,Number obtained by reversing the digits=10x+9-x=9x+9

It is given if 9 is subtracted from the number.,it's digits are interchanged.

90-9x-9=9x+9

81-9x=9x+9

81-9=9x+9x

18x=72

x=72/18

x=4

digits at  ones place is x=4

tens place=9-x=9-4=5

Thus the number  is 54

now it is multiplied by 8

54*8

Thus the no=432

Answer 2

Given:

• Sum of two digits of a number = 9
• If 9 subtracted from the number, the digits interchange their places.

To find:

• Original number?

Solution:

⌬ Let the digit at ones place be x.

Then digit at tens place will be (9 - x)

Therefore,

• The number become = 10(9 - x) + x = 90 - 10x + x = 90 - 9x

Now,

• Number obtained by reversing the digits = 10x + (9 - x) = 9x + 9

⠀⠀ ━━━━━━━━━━━━━━━━━━━━━⠀⠀

★ According to the Question:

➯ (90 - 9x) - 9 = 9x + 9

➯ 81 - 9x = 9x + 9

➯ - 9x - 9x = 9 - 81

➯ - 18x = - 72

➯ 18x = 72

➯ x = 72/18

➯ x = 4

⠀━━━━━━━━━━━━━━━━━━━━━⠀⠀

Therefore,

• Digit at ones place, x = 4
• Digit at tens place, (9 - x) = 9 - 4 = 5

And, When the number is multiplied by 8,

➯ 8 × 54

➯ 432

∴ Hence, the required number is 54.