A dog takes 3 leaps for every 5 leaps of a hare. If one leap of the dog is equal to 3 leaps of the hare, the ratio of the speed of the dog to that of the hare 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 B

Explanation:

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

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:

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}
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}