Rs. 120 are divided among A, B, C such that A's share is Rs. 20 more than B's and Rs. 20 less than C's. What is B's share

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 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 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 B

Explanation:

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