Question

The sum of a two digit number and the number obtained by reversing the order
of the digits is 165. If the digits differ by 3. find the number, when ten's digit
is bigger than the unit's digit.

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Answer 1

The two digits number is 96

Step-by-step explanation:

Let the number of one's place = x

lets the number of ten's place = y

The two digits number will be = 10y+x

Number obtained by reversing the digits = 10x+y

According to question we have

10y+x+10x+y= 165

11x+11y= 165

dividing by 11

x+y=15  ---- (i)

and y-x=3 ----(ii)

⇒y=3+x

substituting the value of y in (i) we get

x+3+x=15

⇒ 2x+3=15

⇒ 2x=15-3

⇒2x=12

⇒x=6

Now substitute the value of x in (ii)

y=3+x

⇒y=6+3=9

Therefore the number will be 10y+x = $10\times 9 + 6 = 96$

#Learn more

On reversing the digits of a two digit number obtained is 9 less than three times the original number. If the difference of these two numbers is 45 find the original number

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