Question

A group of 3 friends staying together consume 54 kg 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:
Here we know that if the number of people increased the same quantity of food grain will last for less number of days. So it is clearly a case of inversion. But since the quantity of food grain is sane we can equate it. so let’s do it!

Complete step by step solution:
Given that a group of 3 friends consume 54kg of wheat every month. That is in 30 days we say.
Now some more friends join this group. Let these new members be x. but they consume the same wheat in 18 days only. So we can write,
\[ \Rightarrow 3 \times 30 = x \times 18\]
To find the value of x,
\[ \Rightarrow x = \dfrac{{3 \times 30}}{{18}}\]
Dividing by 3
\[ \Rightarrow x = \dfrac{{3 \times 10}}{6}\]
Again divide by 3
\[ \Rightarrow x = \dfrac{{10}}{2}\]
\[ \Rightarrow x = 5\]
Thus a new group of friends consist of 5 people.
But we are asked to find the number of new members added. So initially there were 3 friends and now there are 5.
So 2 new members are added.

Note:
Here the thing to note is only that we are asked to find the new members added and not the total number of people in the new group. Thus x is the value of total members in the new group. So subtract the previous members from total members. Simple!