Question

Arya, Abhimanyu and Vivek shared their lunch. Arya has brought two sandwiches, one made of vegetables and one of jam. The other two boys forgot to bring their lunch. Arya agreed to share his sandwiches so that each person will have an equal share of each sandwich.
A. How can Arya divide his sandwiches so that each person has an equal share?
B. What part of a sandwich will each boy receive?

Answer 1

Hint: As each person will have an equal share of sandwiches, Arya will have to divide both the sandwiches into three equal parts (as there are three persons who have to eat it). As Arya shares his sandwiches in equal parts, each boy will receive an equal part of both sandwiches.

Complete step by step solution
We are given that Arya has two sandwiches, one made of vegetable and one of jam. We can represent the same as shown below.

We have been asked to find two conditions as given in the question. Let us consider them.
A. As per the condition, each person should have an equal share, so Arya must divide both his sandwiches into equal parts, that is the vegetable and jam sandwiches must be divided into three equal parts. This can be shown as per the figure below.

B. It is asked here, what part of a sandwich will each boy receive. So, each boy will receive an equal part of both the sandwiches. Now, the vegetable sandwich will be divided into 3 parts. So, we know that 1 sandwich will have 3 parts and each boy will receive 1 part of the sandwich or $\dfrac{1}{3}$ part of the vegetable sandwich. Similarly, jam sandwich is also divided into 3 parts and each boy will receive 1 part of the sandwich or $\dfrac{1}{3}$ part of the jam sandwich too.
Hence, each boy will receive $\dfrac{1}{3}$ part of the vegetable sandwich and $\dfrac{1}{3}$ part of the jam sandwich.

Note: There is a possibility that the students think that the two sandwiches as same and divide the 2 sandwiches in the equal share that is $\dfrac{2}{3}$ parts for each boy. In this way, then each boy can get any sandwich as it will be $\dfrac{2}{3}$ parts of both sandwiches. But it is clearly given in the question that each boy must get equal parts of each sandwich.