1. There are two numbers and their ratio is 3 : 9. If we substract 9 from both numbers then their ratio becomes 12 : 13, what is value is smaller number ?
23
27
31
33
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.
2. 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
4:5
9:5
8:5
9:2
Answer: Option B
Explanation:
Dog : Hare = (3*3) leaps of hare : 5 leaps of hare
= 9 : 5
3. 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
3
4
5
6
Answer: Option A
Explanation:
Let x is subtracted.
Then,
\begin{aligned}
\frac{(6-x)}{(7-x)}< \frac{16}{21} \\