Find the fourth proportion to 2,3,6

Answer: Option D

Explanation:

Let A salary be 2k
B salary be 3k and C salary be 5k

$$\begin{aligned} \text{A's new salary = }\frac{115}{100}*2k \\ = \frac{23}{10}k \\ \text{B's new salary = }\frac{110}{100}*3k \\ = \frac{33}{10}k \\ \text{C's new salary = }\frac{120}{100}*5k \\ = 6k \\ \text{New ratio = }\\ \frac{23k}{10}:\frac{33k}{10}:6k \\ = 23:33:60 \\ \end{aligned}$$

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 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:

$$\begin{aligned} A:B = 2:3 \\ B:C = 4:5 = (4*\frac{3}{4} : 5*\frac{3}{4}) \\ = 3:\frac{15}{4} \\ C:D = 6:7 = (6*\frac{15}{24} : 7*\frac{15}{24}) \\ = \frac{15}{4}:\frac{35}{8} \\ A:B:C:D = 2:3:\frac{15}{4}:\frac{35}{8} \\ = 16:24:30:35 = 8:12:9 \end{aligned}$$

Answer: Option D

Explanation:

From question, lets assume that two numbers are 3x and 5x.

$$\begin{aligned} \text{then, }\frac{3x - 9}{ 5x - 9} = \frac{12}{23}\\ => \text{23(3x - 9) = 12(5x - 9)}\\ => 9x = 99 \\ => x = 11 \end{aligned}$$
So numbers are 3(11) = 33, 5(11) = 55.
Smaller number is 33.