Question

A number consist of two digits.The sum of the digits is 9 .If 45 is subtracted from the number,its digits are interchange . What is the number?
a) 63
b) 72
c) 81
d) 90​

Answer 1

Answer:

72

Step-by-step explanation:

Let two digit no. be 10x + y

x = Tens digit number

y = Units digit number

Given x+y = 9 ---( 1 )

if 45 is subtracted from original number the digits of the original number gets interchanged,

New number will be 10y + x

Thus

10x + y - 45 = 10 y + x

10x - x + y - 10 y = 45

9x - 9y = 45

x - y = 5 --- ( 2 )

From equation 1 and 2

x + y = 9 and x - y = 5 now adding equation 1 and 2 will give,

2x = 14

Thus X = 7

As X + Y = 9

y = 2

Thus your original number will be 72!

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Answer 2

Answer:

63

Step-by-step explanation:

let the unit place of the number be y

let the tenth place of the number be x

terefore the number 10x+y

ATQ

x+y=9 ......eq 1

10x+y -45 = 10y+x .....eq 2

from eq 2

10x+y-45=10y+x

10x-x +y-10y =45

9x-9y =45.....eq 3

substituting the the value of x from eq 1 in eq 3(x=9-y)

9(9-y) -9= 45

81-9y-9=45

72-9y=45

72-45= 9y

27=9y

y=3

putting value of y in eq 1

x+3=9

x=9-3

x=6

the number is 6*10 + 3= 63