The sum of three numbers is 98. If the ratio of the first to the second is 2:3 and that of the second to the third is 5:8, then the second number is

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 B

Explanation:

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

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:

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

Answer: Option A

Explanation:

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