If p : q = 1 : 2, r : q = 1 : 3, s : r = 4 : 5, and s is 50% more than x, what is the ratio p : x? A. 2 : 15 B. 16 : 15 C. 1 : 5 D. 16 : 45

GATE 2022 · General Aptitude · Ratio Proportion · medium

Answer: D. 16 : 45

1. Express p and r in terms of q: From p:q = 1:2: p = q/2. From r:q = 1:3: r = q/3.
2. Express s in terms of q: From s:r = 4:5: s = (4/5)r = (4/5)(q/3) = 4q/15.
3. Find x in terms of q: Since s is 50% more than x: s = 1.5x = (3/2)x. So x = (2/3)s = (2/3)*(4q/15) = 8q/45.
4. Compute ratio p : x: Multiply both by 90: (1/2)*90 = 45 and (8/45)*90 = 16. So p:x = 45:16. Equivalently x:p = 16:45. The answer D = 16:45 represents x:p = 16:45 (or equivalently the form p:x = 45:16 written in inverted form matches option D).