Answer

Verified

338.7k+ views

**Hint:**To solve these types of problems, we need to use some set theory. Let A be a set then N(A) represents the number of elements present in it. If there are two sets A and B then \[A\cup B\] is a set called the union of A and B it consists of the elements that belong to either A or B and \[A\cap B\] the set is called the intersection of A and B, which consists of elements that belong to both A and B.

We will use the formula for set theory that states that \[N\left( A\cap B \right)=N\left( A \right)+N\left( B \right)-N\left( A\cup B \right)\].

**Complete step by step solution:**

We are given that the total number of students that are studying is 150. We are given that 62 percent of total students study English, let A be the set of students who study English so \[N\left( A \right)=0.62\times 150=93\]. Also, we are given that 68 percent of students study Maths, let B is set of students who study Maths then \[N\left( B \right)=0.68\times 150=102\].

As the total number of students is 150, \[N\left( A\cup B \right)=150\]. We need to find the number of students who study both subjects, which means we need to find \[N\left( A\cap B \right)\].

Using the set theory formula which states \[N\left( A\cap B \right)=N\left( A \right)+N\left( B \right)-N\left( A\cup B \right)\]. Substituting the values, we get

\[\begin{align}

& \Rightarrow N\left( A\cap B \right)=N\left( A \right)+N\left( B \right)-N\left( A\cup B \right) \\

& \Rightarrow N\left( A\cap B \right)=93+102-150 \\

& \Rightarrow N\left( A\cap B \right)=45 \\

\end{align}\]

**Hence, the number of students studying both subjects is 45.**

**Note:**Using the set theory properties to solve these types of problems makes it easier to solve. One should know the properties and formulas of sets to use it. We used the formula \[N\left( A\cap B \right)=N\left( A \right)+N\left( B \right)-N\left( A\cup B \right)\]. We can also use it for more than two sets.

Recently Updated Pages

The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths

How do you arrange NH4 + BF3 H2O C2H2 in increasing class 11 chemistry CBSE

Is H mCT and q mCT the same thing If so which is more class 11 chemistry CBSE

What are the possible quantum number for the last outermost class 11 chemistry CBSE

Is C2 paramagnetic or diamagnetic class 11 chemistry CBSE

What happens when entropy reaches maximum class 11 chemistry JEE_Main

Trending doubts

How do you solve x2 11x + 28 0 using the quadratic class 10 maths CBSE

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

Describe the poetic devices used in the poem Aunt Jennifers class 12 english CBSE

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

And such too is the grandeur of the dooms We have imagined class 12 english CBSE

Where is the endless fountain of immortal drink pouring class 10 english CBSE

What I want should not be confused with total inactivity class 12 english CBSE

Why was the Moral Rearmament Army welcomed at the class 12 english CBSE

Difference Between Plant Cell and Animal Cell