Question

Two cats Billy and Kitty together catch $60$ mice. If Billy catches three mice for every two caught by Kitty, the number of mice caught by Kitty is.
(a) $24$
(b) $30$
(c) $36$
(d) $40$

Answer 1

Hint: In this numerical, we have to use the concept ratio.
Ratio is nothing but the comparison of two numbers which are identical in units.
For e.g. comparison between pencil’s length and pen’s length. The unit is the same for both that is distance. Here also, we have to compare the mice caught by Billy and Kitty (Two cats) and simplify the equation for getting the answer.

Complete step-by-step solution:
Given that, there are two cats named Billy and Kitty.
These two cats catch $60$ mice together.
Whereas Billy catches three mice for every two caught by Kitty.
Now, we have to find how many mice have been caught by Kitty.
So, it is given that, Billy catches $3$ mice over the $2$ mice caught by Kitty then we can write it as,
The ratio of mice which has been caught by Billy and Kitty $=3:2$
Let $x$ mice caught by Kitty and Billy then we can write it as, $\dfrac{3}{x}=\dfrac{2}{x}$
Thus we can write it in the equation form as,
$\Rightarrow$$3x+2x=60$
As the $3x$ mice caught by Billy and $2x$ mice caught by Kitty and both the cats caught $60$ mice together.
Simplify the equation, we get,
$\Rightarrow$$5x=60$
$\Rightarrow$$x=\dfrac{60}{5}$
$\Rightarrow$$x=12$
But, as we already discussed above, the number of mice caught by Kitty is $=2x$
$=2\times 12$
$=24$
Hence, the number of mice caught by Kitty is $24,$

Therefore option $(a)$ is correct.

Note: The comparison of two elements with the same unit is known as ratio.
Here we are using the concept of ratio.
So, while performing concept of ratio we should note some points such as,
The ratio we are taking should be of the same kind.
When we are comparing two elements. We have to use a similar unit.
The comparison of ratios can only be achieved when the ratios are equivalent such as fractions.
The symbol used for showing the ratio is $':'$