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NDA 2023
Exam
NDA
Year
2023
Subject
Mathematics
Chapter
Statistics

NDA 2023 · Mathematics · Statistics

The central angles p, q, r and s (in degrees) of four sectors in a...

The central angles p,q,rp, q, r and ss (in degrees) of four sectors in a Pie Chart satisfy the relation 9p=3q=2r=6s9 p=3 q=2 r=6 s. What is the value of 4p−q4 p-q ?

Options

  1. A1212
  2. B2424
  3. C3030
  4. D3636

Correct answer

D. 3636

Step-by-step solution

p+q+r+s=360∘p+q+r+s=360^{{}^{\circ}} ....(1)
p=k9,q=k3,r=k2,s=k6p=\frac{k}{9}, q=\frac{k}{3}, r=\frac{k}{2}, s=\frac{k}{6} From (1), k9+k3+k2+k6=360∘⇒2k+6k+9k+3k18=360∘⇒20k=360∘×18⇒k=324∘∴4p−q=4k9−k3=k9=3249∴4p−q=36∘\frac{k}{9}+\frac{k}{3}+\frac{k}{2}+\frac{k}{6}=360^{{}^{\circ}}\Rightarrow \quad \frac{2 k+6 k+9 k+3 k}{18}=360^{{}^{\circ}}\Rightarrow \quad 20 k=360^{{}^{\circ}} \times 18 \Rightarrow \mathrm{k}=324^{{}^{\circ}}\therefore \quad 4 p-q=\frac{4 k}{9}-\frac{k}{3}=\frac{k}{9}=\frac{324}{9}\therefore \quad 4 p-q=36^{{}^{\circ}}
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