Question

The middle digit of a number between 100&1000 is0.the sum of the other digit is13.if the digit be reversed ,the number so formed exeeds the original number by 495 find the number

Answer 1

409 here is your answer

Answer 2

Answers

sivaprasath Ace

Solution:

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