From second constraint, 
OLD Visitors = x, MID = 2x, Young = 4x. 
7x = 140 or, x = 20 , 2x = 40 , 4x = 80. 
Let us fill this in. and then go to constraint 3 and 4.

From constraint 3, Total Platinum = 2y, then YNG platinum should be y. 
From constraint 4, Let us fill OLD-GOLD and OLD-ECO has z.

Let us go statement-by-statement and see if we can find some easy one that HAS to be FALSE. 
(A) The numbers of Gold and Platinum tickets bought by Young visitors were equal. 
YNG-PT = YNG-GOLD. These two should add up to 42. Or, both should be 21. Total PT should be
42. Total GOLD should be 43. 
All of these appear to be possible. Let us look at the other choices and see if we can find an easier
CLEARLY FALSE statement. 
Else, we will revisit this.

(B) The numbers of Middle-aged and Young visitors buying Gold tickets were equal. 
MID-GOLD = YNG-GOLD. MID-GOLD should also be 42 – y. This tells us that z should be 1. This
also appears prima-facie possible. 
Let us look at the others also before we revisit this one and completely fill the grid.

(C) The numbers of Old and Middle-aged visitors buying Economy tickets were equal. 
OLD-ECO = MID-ECO.These two should add up to 17 so these two CANNOT be equal. 
So, statement C is DEFINITELY FALSE. 
(D) The numbers of Old and Middle-aged visitors buying Platinum tickets were equal. 
OLD-PT = MID-PT. Both of these should be y2𝑦2. This also appears to be alright.