1.

The middle digit of a number between 100 and 1000 is zero, and the sum of other digits is 11. Ifthe digits are reversed, the number so formed exceeds the orginal number by 495. Find the number​

Answer»

Answer:

308

Step-by-step explanation:

Let the number in 100S digit be X,

Let the number in 1s digit be y,

 

Then,the number would be x0y : 100x+y

Condition 1: Sum of the digits : x+y=11.....(i)

If it is reversed ,it would be y0x : 100y+x,

The DIFFERENCE between them:    100x+y -(100y+x) = -495

                                                       100x+y-100y-x =-495

                                                        99x-99y  = -495  (divided by 99)

                                                        x-y=-5.....(ii)              

Adding (i) and (ii), we get,

                                (x+y)+(x-y)=11+(-5)

                                     x+y+x-y=11-5

                                               2x=6

                                              ∴ x=3

Substituting value of x in (i),

                                          x+y=11

                                          3+y=11

                                              y=11-3

                                           ∴ y=8

                             ∴The number is 308

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