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:

In this type of question, we will first try to calculate the ratio of two persons. Once we get ratio then we can easily get our answer. So lets solve this.

\begin{aligned}
\frac{4}{15}A = \frac{2}{5}B \\
A = \left(\frac{2}{5}*\frac{14}{4}\right)B \\
A = \frac{3}{2}B \\
\frac{A}{B} = \frac{3}{2} \\
A:B = 3:2 \\
\text{B's Share = }\frac{2}{5}*1210 = 484
\end{aligned}

Answer: Option B

Explanation:

Let C = x. Then A = (x—20) and B = (x—40).
x + x - 20 + x - 40 = 120 Or x=60.
A:B:C = 40:20:60 = 2:1 :3.
B's share = Rs. 120*(1/6) = Rs. 20

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 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 D

Explanation:

Let the first number is A and second number is B.

As per question

\begin{aligned}
\frac{40}{100}A = \frac{2}{3}B \\

\frac{A}{B} = \frac{2}{3}*\frac{100}{40} \\
\frac{A}{B} = \frac{5}{3} \\
=> A:B = 5:3

\end{aligned}