Question

the sum of the digit of a 2 - digit number is11 the number obtained by interchaning the digits exceeds the original number by 27 find the number​

Answer 1

Answer:

let no. be 10y+x

given x+y=11

x=11-y [equation 1]

after interchanging digits, new no.= 10x+y

10y+x+27= 10x+y

27= 10x-x+y-10y

27=9x-9y

27=9(x-y)

x-y= 27/9= 3

x= 3+y [equation 2]

comparing equations 1 and 2

11-y=3+y

11-3=y+y

8= 2y

y= 8/2

y= 4

from equation 2

x= 3+4

x=7

original no.= 10y+x

=40+7

=47

Answer 2

AnswEr :-

• Original number is 47.

Given :-

• The sum of the digit of a two digit number is 11. The number obtained by interchanging the digits exceeds the original number by 27.

To Find :-

• The original number.

SoluTion :-

Let,

• Digit at ones place be x

• Digit at tens place be 11 - x

» Original number :-

→ 10 (11 - x) + x × 1

→ 110 - 10x + x

→ 110 - 9x

» After interchanging the digits :-

→ 10x + 1 (11 - x)

→ 10x + 11 - x

→ 11 + 9x

★ New number exceeds the original number by 27.

Now,

» According to question :-

→ (9x + 11) - (110 - 9x) = 27

→ 9x + 11 - 110 + 9x = 27

→ 18x - 99 = 27

→ 18x = 99 + 27

→ 18x = 126

→ x = 126/18

→ x = 7

Original no. → 110 - 9x → 110 - 9(7) → 110 - 63 → 47

Hence, the original number is 47.

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