Question

# In a zoo, deer and lion are in the ratio of 5:2. If there are 20 deer, then how many lions are there?(a) 4(b) 6(c) 8(d) 10

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Hint: Whenever there is a ratio a:b, it means there exist a common factor x which is unknown such that $ax = bx$, where $ax$ is the actual count of first object and $bx$ is the count of second object.
The ratio $\dfrac{a}{b}$ is same as the ratio $\dfrac{{ax}}{{bx}}$ with the common factor x getting cut off, where the numerator gives the actual count of first object and the denominator giving the count of second.
Initial idea is obtained by looking into each option and matching it with the given data of count of deer which is the trial and error method.

Converting given ratio to actual count,
Here the ratio is 5:2
Thus there exists an unknown factor x such that $5x = 2x$, where 5x denotes the number of deer and 2x represents the number of lions. Thus finding x solves the problem.
Equate the number of deer to given value 20, to find x.
Number of deer = 20,
Implies 5x=20
x=4
Step3: Now to find the number of lions, substitute the value of x=4 in 2x which is the count of lions in terms of x.
$2x = 2(4) = 8$
We obtain, Number of Lions=8

So, the correct answer is “Option C”.

Additional Information: The above procedure can be repeated for three or more object ratios as below:
If we have the ratio a:b:c implies that there exists a common factor x such that ax gives the actual count of the first object, bx gives the second and cx gives the third.
After computing the actual count of objects, it must be made sure to match the counts to appropriate objects.

Note: Students many times make mistakes when ratio is not given in simplest form and they start solving the question, always keep in mind first cut all the common factors between the numerator and denominator in the ratio and then solve else calculations will be more complex.