GATE 2022 PH – Question 3
If p:q=1:2, q:r=4:3, r:s=4:5, and u is 50% more than s, what is p:u?
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Correct answer: (D) 16: 45
Explanation
Write every quantity in terms of $p$.
- $p:q=1:2\Rightarrow q=2p$.
- $q:r=4:3\Rightarrow r=\tfrac34q=\tfrac32p$.
- $r:s=4:5\Rightarrow s=\tfrac54r=\tfrac{15}{8}p$.
- $u$ is 50% more than $s$: $u=1.5s=\tfrac32\cdot\tfrac{15}8p=\tfrac{45}{16}p$.
Taking $p=16$ gives $q=32$, $r=24$, $s=30$ and $u=45$.
$$p:u=16:45\quad(\text{option D}).$$