Question

A group of 3 friends staying together, consume 54kg of wheat every month. Some more friends join this group and they find that the same amount of wheat lasts for 18 days. How many new members are there in this group now?

Answer 1

Hint: Assume the number of new members in the group as ‘n’. Consider two cases, in the first case consider the number of members in the group as 3 and find the quantity of wheat consumed by 1 person in one day using the given information. In the second case consider the number of members in the group as (n + 3) and find the quantity of wheat consumed by 1 person in one day using the given information. Now, equate the two expressions obtained and find the value of ‘n’ to get the answer.

Complete step-by-step answer:
Here, let us assume that the number of new members added in the group of 3 friends is ‘n’. Therefore, the total numbers of members in the group becomes (n + 3). Now, we have been given two cases regarding the consumption of wheat, so let us check them one – by – one.
Case 1: - When there was a group of 3 friends: -
Here, in this case we have been given that they consume 54kg of wheat in one month. Therefore, we have,
\[\Rightarrow \] Wheat consumed by 3 friends in 30 days = 54kg
\[\Rightarrow \] Wheat consumed by 1 friend in 30 days = \[\dfrac{54}{3}\]kg = 18kg
\[\Rightarrow \] Wheat consumed by 1 friend in 1 day = \[\dfrac{18}{30}\]kg = \[\dfrac{3}{5}\]kg – (1)
Case 2: - When ‘n’ more friends are added and the total number of members become (n + 3): -
Here, in this case we have been given that they consume 54kg of wheat in 18 days. Therefore, we have,
\[\Rightarrow \] Wheat consumed by (n + 3) friends in 18 days = 54kg
\[\Rightarrow \] Wheat consumed by 1 friend in 18 days = \[\dfrac{54}{n+3}\]kg
\[\Rightarrow \] Wheat consumed by 1 friend in 1 day = \[\dfrac{54}{\left( n+3 \right)\times 18}\]kg – (2)
Now, the quantity of wheat consumed by one person in both the cases must be the same. So, equating equations (1) and (2), we get,
\[\begin{align}
  & \Rightarrow \dfrac{3}{5}=\dfrac{54}{\left( n+3 \right)\times 18} \\
 & \Rightarrow \dfrac{3}{5}=\dfrac{3}{\left( n+3 \right)} \\
\end{align}\]
Cancelling 3 from the numerator of both sides, we get,
\[\Rightarrow \dfrac{1}{5}=\dfrac{1}{\left( n+3 \right)}\]
By cross – multiplication, we get,
\[\begin{align}
  & \Rightarrow n+3=5 \\
 & \Rightarrow n=2 \\
\end{align}\]
Hence, two new members are there in the group now.

Note: One may note that the quantity of wheat consumed by each friend in one day will be the same in both cases because the total quantity of wheat consumed remains same but the number of friends got increased and hence the number of days for the consumption of total weight of wheat gets decreased. You can see that we have used the basic approach of the unitary method to solve the question because we do not have any direct formula and so we need to proceed step – by – step.