The least whole number which when subtracted from both the terms of the ratio 6 : 7 to give a ratio less than 16 : 21, is

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:

\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:

\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:

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

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}