GATE 2022 BT – Question 3

General Aptitude · Quantitative Aptitude: Arithmetic and Number Computation · 1 mark · Multiple choice

If $p:q=1:2$, $q:r=4:3$, $r:s=4:5$ and u is 50% more than s, what is $p:u$?

2 ∶15
16 ∶15
1: 5
16: 45

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Correct answer: (D) 16: 45

Explanation

Express every quantity in terms of $p$.

$p:q=1:2\Rightarrow q=2p$.
$q:r=4:3\Rightarrow r=\dfrac34q=\dfrac34(2p)=\dfrac32p$.
$r:s=4:5\Rightarrow s=\dfrac54r=\dfrac54\cdot\dfrac32p=\dfrac{15}{8}p$.
$u$ is 50% more than $s$: $u=1.5s=\dfrac32\cdot\dfrac{15}{8}p=\dfrac{45}{16}p$.

**Ratio:**
$$p:u=p:\frac{45}{16}p=1:\frac{45}{16}=\mathbf{16:45}.$$