If Rs. 782 is divided into three parts, proportional to
\begin{aligned}
\frac{1}{2}:\frac{2}{3}:\frac{3}{4}
\end{aligned}

find the first part.

Answer: Option A

Explanation:

\begin{aligned}
a:b = 2:3 \\
b:c = 4:3 = (4*\frac{3}{4} : 3*\frac{3}{4}) \\
= 3:\frac{9}{4} \\
a:b:c = 2:3:\frac{9}{4} \\
= 8:12:9
\end{aligned}

Answer: Option B

Explanation:

Dog : Hare = (3*3) leaps of hare : 5 leaps of hare
= 9 : 5

Answer: Option C

Explanation:

2:3 :: 6:x

=> 2/3 = 6/x
=> x = 18/2
=> x = 9

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 B

Explanation:

\begin{aligned}
\frac{1}{2}:\frac{2}{3}:\frac{3}{4} \\
= 6:8:9\\
\text{First part =} 782 * \frac{6}{23} \\
= 204
\end{aligned}