Question

In a class of 70 all like to play kabaddi and kho kho. 45 like to play kabaddi and 52 khokho. How many students like to play kabaddi or khokho?

Answer 1

Hint: We will assume that the number of students who like to play both kabaddi and kho kho is x. The number of students who like to play kabaddi will be (45-x) and the number of students who like to play kho kho will be (52-x). And it is given in the question that the total number of students is 70. So, we will form an equation, (45-x) + (52-x) + x = 70. We will solve this equation to get the value of x.

Complete step-by-step answer:
It is given in the question that in a class of 70 all like to play kabaddi and kho kho. 45 like to play kabaddi and 52 khokho. And we have been asked to find the number of students who like to play kabaddi or khokho.
Let us assume that the number of students who like to play both kabaddi and kho kho is x. We know that 45 students like to play kabaddi and 52 students like to play kho kho.
So, we will get the number of students who like to play only kabaddi as (45-x) and the number of students who like to play only kho kho as (52-x).
Now, we can represent the given information in a Venn diagram as follows.

We know that the total number of students in the class is 70. So, we can write,
(45-x) + (52-x) + x = 70
45 – x + 52 – x + x = 70
On simplifying it, we get,
97 – x = 70
On transposing 97 from the LHS to RHS, we get,
- x = 70 – 97
- x = - 27
On multiplying both the sides with (-1), we get,
x = 27
Thus, the number of students who like both kabaddi and kho kho is 27.

Note: Most of the students may mistake while writing the final equation, they may write it as, (45+x) + (52+x) + x = 70, but this is wrong as we have to subtract the common students from the list of students who like only one of the games as they are repeating. Also, after finding the value x, one can find the number of students who like to play only kabaddi as (45-x) = (45-27) = 18 and the number of students who like to play only kho kho as (52-x) = (52-27) = 25.