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 ?

Previously Asked in : Gate CE-forenoon season 2022 ||

1 : 5

16 : 45

2 : 15

16 : 15

Answer (Detailed Solution Below)

Option 16 : 45 is correct

Detailed Explanation :

Given \dfrac {p} {q} = \dfrac {1} {2}, \dfrac {q} {r} = \dfrac {4} {3}, \dfrac {r} {s} = \dfrac {4} {5}

\Rightarrow \dfrac {r} {s} = \dfrac {4 \times 3} {5 \times 3}

\Rightarrow \dfrac {q} {r} = \dfrac {4 \times 4} {3 \times 4}

\Rightarrow \dfrac {p} {q} = \dfrac {1 \times 8} {2 \times 8 }

From above p : q : r : s \\8 : 16 : 12 : 15

\therefore \, s = 15\\ \textrm{so} \, u = 15 \times 15 = 22.5

now \dfrac {p} {q} = \dfrac {8} {22.5}

= \dfrac {80} {225} = \dfrac {16} {45}

Correct option is : 16 : 45

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