Question

Sum of the digits of a two digit number is 9. When we interchange the digits, it is found that the resulting new number is greater than the original number by 63. Find the two digit number. please send answer​

Answer 1

Answer:

let the unit digit of no. be x

so, tens digit = 9-x

thus the original no. will be = (10*tens)+unit digit

=> (10*9-x)+x

= 90-10x+x

= 90-9x

now, the no. obtained if we interchanged the digit-

=> (10*x)+9-x

= 10x+9-x

= 9x+9

given, the resulting new no. is greater than original no. by 63 so,

=> 90-9x+63=9x+9

= 90+63-9x=9x+9

= 153-9x=9x+9

= 153-9=9x+9x

= 144=18x

=> x= 144/18

=> x=8

therefore the original no. will be-

=> 90-9(8)

= 90-72

= 18

so, original no. is 18

Step-by-step explanation:

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Answer 2

Answer:

The number is 18

Explanation by easiest method:-

Let the unit's digit be y and ten's digit be x

=> x+y=9 ……… (i)

After we interchange the digits

=> 10y+x=10x+y+63…………(n)

=> 9y-9x=63

=> y-x=7……… (ii)

Now, x+y=9 and y-x=7

=> x+y+y-x=9+7

=>2y=16

=>y=8

=>x+y=9

=>x+8=9

=>x=1

Therefore, the no. is 10x+y=10×1+8=10+8=18

You can check the answer by replacing the value in equation(n)

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