GATE Civil 2022 Set 1 | GA Question: 3

Question

If

$p : q = 1:2$

$q : r = 4 : 3$

$r : s = 4 : 5$

and $u$  is $50\%$ more than $s$, what is the ratio $p : u$?

• A. $2 : 15$
• B. $16 : 15$
• C. $1 : 5$
• D. $16 : 45$

Answer 1

Upon finding ratio between p:q:r:s we will get 8:16:12:15 ... now we know that u is 50% more than s , let suppose s is 15x then u would be 22.5x ... thus p:u becomes 8:22.5 .... on solving this we will get 16:45 which is correct ans to this question.

Answer 2

Given that,

• $p:q = 1:2$
• $q:r = 4:3$
• $r:s = 4:5$

Let, $p:q = 1:2 = k \Rightarrow \boxed{p = k,q = 2k}$

And, $r:s = 4;5 = k \Rightarrow \boxed{r = 4k, s = 5k}$

Now, $u = 5k \times 1.5 = 7.5k$

$\therefore $ The ratio of $p:u = k:7.5k = 1:7.5 = 2:15.$

Correct Answer $:\text{A}$

${\color{Green}{\textbf{PS:} \; \text{If}\;x \;\text{is}\; 50\%\;\text{more than}\; 100 \Rightarrow x = 100 + 100 \times \frac{50}{100} = 150.}}$