In a college, the ratio of the number of boys to girls is 8 : 5. If there are 200 girls, the total number of students in the college is

Answer: Option D

Explanation:

Let A = 2x, B = 3x, C = 4x, then,
\begin{aligned}
\frac{A}{B} = \frac{2x}{3x} = \frac{2}{3} \\
\frac{B}{C} = \frac{3x}{4x} = \frac{3}{4} \\
\frac{C}{A} = \frac{4x}{2x} = \frac{2}{1} \\

=> \frac{A}{B}:\frac{B}{C}:\frac{C}{A} \\
= \frac{2}{3}:\frac{3}{4}:\frac{2}{1} \\
= 8:9:24


\end{aligned}

Answer: Option C

Explanation:

Let the third number be x.
First Number (120/100)*x = 6x/5
Second Number (150/100)*x = 3x/2

Ratio = 6x/5:3x/2
=> 4:5

Answer: Option D

Explanation:

\begin{aligned}
a:b = 2:3 \\
b:c = 5:8 = (5*\frac{3}{5} : 8*\frac{3}{5}) \\
= 3:\frac{24}{5} \\
a:b:c = 2:3:\frac{24}{5} \\
= 10:15:24 \\
b = 98*\frac{15}{49} \\
= 30
\end{aligned}

Answer: Option B

Explanation:

Let the boy are 8x and Girls are 5x

=> 5x = 200
=> x = 40

Total students = 8x+5x = 13x = 13(40) = 520

Answer: Option C

Explanation:

Treat 2:9 as 2/9 and x:18 as x/18, treat :: as =

So we get 2/9 = x/18
=> 9x = 36
=> x = 4