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 D

Explanation:

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

As per question

$$\begin{aligned} \frac{40}{100}A = \frac{2}{3}B \\ \frac{A}{B} = \frac{2}{3}*\frac{100}{40} \\ \frac{A}{B} = \frac{5}{3} \\ => A:B = 5:3 \end{aligned}$$

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 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.

Answer: Option C

Explanation:

Let the original Salaries of Ravi and Sumit is 2x and 3x.

So as per question

$$\begin{aligned} \frac{2x+4000}{3x+4000} = \frac{40}{57} \\ => 57(2x+4000) = 40(3x+4000) \\ => 6x = 68000 \\ => 3x = 34000 \\ \text{ Sumit Salary =} 3x+4000 \\ 34000 + 4000 = 38000 \end{aligned}$$