(1) The research funds received by departments X and Y were in the ratio 3 to 5, respectively.
X : Y = 3 : 5 | For every $3x received by department X, department Y receives $5x. Since we
have no information about the funds received by department Z, we can't say for sure which of
the three departments gets the maximum funds Insufficient

(2) The research funds received by departments X and Z were in the ratio 2 to 1, respectively.
X : Z = 2 : 1 | For every $2y received by department X, department Z receives $y. Since we
have no information about the funds received by department Y, we can't say for sure which of
the three departments gets the maximum funds Insufficient

When we combine the information present in both the statements,
X:Y = 3:5 and X:Z = 2:1 -> X:Y:Z = 6:10:3. We can clearly see that
the department Y gets the maximum funds (Sufficient - Option C)
_________________

IMO C
Y has greatest proportion
3 to 5 to 1.5

hello pushpitkc hope you are having a cool summer weekend

have some questions

\(\frac{3x}{5y}\) \(\frac{2x}{1y}\)

so here i see a common value - i mean X so i mupltiply 3x by 2x and 5y by 2x so i get \(\frac{6x}{10y}\) after this i got confused i bit

two questions how did you get 3 here 6:10:3

and how did you assign values X:Y:Z = 6:10:3 respectively ?

thanks