Question

The $6$ dozen eggs are bought for $Rs.108$. How much will $108$ eggs cost?
A. $Rs.\,171$
B. $Rs.\,162$
C. $Rs.\,153$
D. $Rs.\,180$

Answer 1

Hint: Here it is given that $6$ dozen eggs are bought for $Rs.108$ and we have to determine the cost of $108$ eggs. In order to calculate the cost of $108$ we will use the given data and calculate the cost that $1$ dozen of eggs comprises and then we will convert $108$ eggs into dozens by the relation $1$ dozen $ = 12$.

Complete step by step answer:
Here it is given that $6$ dozen eggs are bought for $Rs.108$ and we have to determine the cost of $108$ eggs. So, we have
Cost of $6$ dozen eggs $ = Rs.\,108$
Now, we will calculate the cost of $1$ dozen eggs. The cost of $1$ dozen eggs can be calculated by dividing $108$ by $6$. So,
Cost of $1$ dozen eggs $ = \dfrac{{108}}{6}$

On dividing we get, Cost of $1$ dozen eggs $ = Rs.18$
Now, we will convert $108$ eggs into dozens by the relation $1$ dozen $ = 12$.
For converting $108$ eggs into dozens we divide $108$ by $12$.
So, $108$ eggs $ = \dfrac{{108}}{{12}} = 9$
Now, we will calculate the cost of $9$ dozen eggs.
Cost of $9$ dozen eggs $ = 9 \times 18 = Rs.162$
Therefore, the cost of $108$ eggs is $Rs.\,162$.

Hence, option B is the correct answer.

Note: In order to solve these types of problems we should know the concept of ratio and proportions. By determining the cost of one dozen eggs we can calculate the cost of how many eggs by just multiplying them. We should always know the meaning of general terms of measuring quantity such as a dozen in this case. Dozen is one of the most important groupings used for measurements in day- to- day life and there are other similar quantities of measurements like gross which is equal to $12$ dozens or $144$ items.