17 The sum of a two-digit number and the number formed by interchangin

1.	17 The sum of a two-digit number and the number formed by interchanging its digit is 110. If 10 issubtracted from the original number, the new number is 4 more than 5 times the sum of thedigits of the original number. Find the original number
Answer» Let the unit digit be y & tens digit be x. Original number = (10x+y) After interchanging the digits New number = (10y+x) (10x+y) + (10y+x) = 110 11x +11y = 110 11(x+y)= 110 x+y = 110/11 x+y= 10…………...(1) x= 10-y……………(2) (10x+y) - 10 = 4+ 5(x+y) (10x+y) - 10 = 4+ 5(10) (10x+y) = 4+ 50+10 (10x+y) = 64 10(10-y) +y = 64 100-10y +y= 64 100 -9y = 64 -9y = 64-100 -9y = -36 y= 36/9= 4 y= 4 putting the value of y in eqn 2 x= 10-y x= 10-4 x= 6 Hence , the first number is 6 & second number is 4. Original Number is 10x+y = 10× 6+4= 60+4= 64 Hit like if you find it useful!

17 The sum of a two-digit number and the number formed by interchanging its digit is 110. If 10 issubtracted from the original number, the new number is 4 more than 5 times the sum of thedigits of the original number. Find the original number

Answer»

Let the unit digit be y & tens digit be x.

Original number = (10x+y)

After interchanging the digits

New number = (10y+x)

(10x+y) + (10y+x) = 110

11x +11y = 110

11(x+y)= 110

x+y = 110/11

x+y= 10…………...(1)

x= 10-y……………(2)

(10x+y) - 10 = 4+ 5(x+y)

(10x+y) - 10 = 4+ 5(10)

(10x+y) = 4+ 50+10

(10x+y) = 64

10(10-y) +y = 64

100-10y +y= 64

100 -9y = 64

-9y = 64-100

-9y = -36

y= 36/9= 4

y= 4

putting the value of y in eqn 2

x= 10-y

x= 10-4

x= 6

Hence , the first number is 6 & second number is 4.

Original Number is 10x+y = 10× 6+4= 60+4= 64

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