Question

35.The digits of a 2-digit number differ by 5. If the digits are interchanged and the resulting number is added to the original number, we get 99. Find the original number.

Answer 1

Answer:

54 and 45

Step-by-step explanation:

54 + 45 =99

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Answer 2

let the ten's digit=x and let the unit digit=y

then the number=10x+y

x-y=5(given)(equation 1)

10x+y+10y+x=99

11x+11y=99

dividing 11 from both sides

11(x+y)=11(9)

we get

x+y=9(equation 2)

subtract eq 1 from eq 2

we get

x+y-(x-y)=9-5

x+y-x+y=4

2y=4

y=2

putting value of y in eq 1

x-y=5

x-2=5

x=5+2

x=7

hence, the no. is

number=10x+y

number=10(7)+2

number=70+2

number=72

checking

in equation 1

x-y=5

7-2=5

5=5

in equation 2

x+y=9

7+2=9

9=9

11x+11y=99

11(7)+11(2)=99

77+22=99

99=99

hence the answer is correct

number=72

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