Question

Find the number of women who like both ruby and diamond.

• A. 30
• B. 32
• C. 12
• D. 6
• E. 18

Answer 1

The correct option is A 30

Diamond $=\frac{600\times 40}{100}=240$
Ruby $=\frac{600\times 20}{100}=120$
Emerald $=\frac{600\times 10}{100}=60$
Diamond and Ruby $=\frac{600\times 5}{100}=30$
Ruby and Emerald = $=\frac{600\times 3}{100}=18$
Emerald and Diamond $=\frac{600\times 4}{100}=24$
Diamond, Emerald and Ruby $=\frac{600\times 2}{100}=12$
$\therefore a+d+e+f=240$
$\Rightarrow b+d+e+g=120$
$\Rightarrow c+f+e+g=60$
$\Rightarrow d+e=30$
$\Rightarrow e+g=18$
$\Rightarrow e+f=24$
$\Rightarrow e=12$
$\therefore f=24-12=12g=18-12=6d=30-12=18c=60-12-12-6=30$
$\therefore b=120-30-6=84$
$\therefore a=240-30-12=198$

Number of women who like both Ruby and diamond $=30$