Here first of all i would like to notice you that the answer provided above is not Wrong . May be the options given to you May have been wrong. kindly Note it
When 2 solutions of molarities M1 and M2 and volumes V1 and V2 are mixed together, the new molarity M is equal to,
M= (M1V1+ M2V2)/ (V1+V2)
We have, Normality= Molarity* Acidity or Basicity
Since HCl is a monobasic acid, or a monoprotic acid, that is it releases only 1 hydronium ion in solution, it's normality= molarity* 1
So normality and molarity are equal in this case.
therefore rearranging the above equation, we get
the total volume, (V1+V2)= (M1V1+ M2V2) / M
= (N1V1 + N2V2) / N
= (2* 500 + 5*500) / 3
= 3500/ 3
= 1166 mL