In a group of 500 people, 200 can speak Hindi alone while only 125 speak English alone. The number of people who can speak both Hindi and English is
$
{\text{A}}{\text{. 175}} \\
{\text{B}}{\text{. 325}} \\
{\text{C}}{\text{. 300}} \\
{\text{D}}{\text{. 375}} \\
$
Last updated date: 19th Mar 2023
•
Total views: 305.4k
•
Views today: 3.84k
Answer
305.4k+ views
Hint: Here, we will proceed by drawing the relevant Venn diagram according to the problem statement and then finding out the value of the unknown regions by visually analysing the diagram.
Complete step-by-step answer:
Given, there are total 500 number of people in the group who can speak either English or Hindi or both Hindi and English (this region is represented by all the three coloured lines which are blue, green and red lines in the figure or the complete region of the figure) i.e., $n\left( {E \cup H} \right) = 500$
Also given that 200 number of people can speak Hindi alone (this region is represented by red coloured lines in the figure) i.e., $n\left( {H{\text{ only}}} \right) = 200$
Also given that 125 number of people can speak English alone (this region is represented by blue coloured lines in the figure) i.e., $n\left( {E{\text{ only}}} \right) = 125$
We have to find the number of people who can speak both Hindi and English (this region is represented by green coloured lines in the figure) i.e., $n\left( {E \cap H} \right)$
Clearly from the Venn diagram shown, we can write
Total region which consists of all the coloured lines which includes blue, green and red coloured lines is equal to the sum of the region which consists of blue coloured lines, the region which consists of green coloured lines and the region which consists of red coloured lines.
$
\Rightarrow n\left( {E \cup H} \right) = n\left( {E{\text{ only}}} \right) + n\left( {E \cap H} \right) + n\left( {H{\text{ only}}} \right) \\
\Rightarrow n\left( {E \cap H} \right) = n\left( {E \cup H} \right) - n\left( {E{\text{ only}}} \right) - n\left( {H{\text{ only}}} \right) = 500 - 125 - 200 \\
\Rightarrow n\left( {E \cap H} \right) = 175 \\
$
Therefore, the total number of people who can speak both Hindi and English are 175
Hence, option A is correct.
Note: In this particular problem, the total number of people who can speak Hindi (this region is represented by two coloured lines which are red and green) is $n\left( H \right) = 200 + 175 = 375$ and the total number of people who can speak English (this region is represented by two coloured lines which are blue and green) is $n\left( E \right) = 125 + 175 = 300$.
Complete step-by-step answer:

Given, there are total 500 number of people in the group who can speak either English or Hindi or both Hindi and English (this region is represented by all the three coloured lines which are blue, green and red lines in the figure or the complete region of the figure) i.e., $n\left( {E \cup H} \right) = 500$
Also given that 200 number of people can speak Hindi alone (this region is represented by red coloured lines in the figure) i.e., $n\left( {H{\text{ only}}} \right) = 200$
Also given that 125 number of people can speak English alone (this region is represented by blue coloured lines in the figure) i.e., $n\left( {E{\text{ only}}} \right) = 125$
We have to find the number of people who can speak both Hindi and English (this region is represented by green coloured lines in the figure) i.e., $n\left( {E \cap H} \right)$
Clearly from the Venn diagram shown, we can write
Total region which consists of all the coloured lines which includes blue, green and red coloured lines is equal to the sum of the region which consists of blue coloured lines, the region which consists of green coloured lines and the region which consists of red coloured lines.
$
\Rightarrow n\left( {E \cup H} \right) = n\left( {E{\text{ only}}} \right) + n\left( {E \cap H} \right) + n\left( {H{\text{ only}}} \right) \\
\Rightarrow n\left( {E \cap H} \right) = n\left( {E \cup H} \right) - n\left( {E{\text{ only}}} \right) - n\left( {H{\text{ only}}} \right) = 500 - 125 - 200 \\
\Rightarrow n\left( {E \cap H} \right) = 175 \\
$
Therefore, the total number of people who can speak both Hindi and English are 175
Hence, option A is correct.
Note: In this particular problem, the total number of people who can speak Hindi (this region is represented by two coloured lines which are red and green) is $n\left( H \right) = 200 + 175 = 375$ and the total number of people who can speak English (this region is represented by two coloured lines which are blue and green) is $n\left( E \right) = 125 + 175 = 300$.
Recently Updated Pages
Calculate the entropy change involved in the conversion class 11 chemistry JEE_Main

The law formulated by Dr Nernst is A First law of thermodynamics class 11 chemistry JEE_Main

For the reaction at rm0rm0rmC and normal pressure A class 11 chemistry JEE_Main

An engine operating between rm15rm0rm0rmCand rm2rm5rm0rmC class 11 chemistry JEE_Main

For the reaction rm2Clg to rmCrmlrm2rmg the signs of class 11 chemistry JEE_Main

The enthalpy change for the transition of liquid water class 11 chemistry JEE_Main

Trending doubts
Difference Between Plant Cell and Animal Cell

Write an application to the principal requesting five class 10 english CBSE

Ray optics is valid when characteristic dimensions class 12 physics CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

Write the 6 fundamental rights of India and explain in detail

Write a letter to the principal requesting him to grant class 10 english CBSE

List out three methods of soil conservation

Fill in the blanks A 1 lakh ten thousand B 1 million class 9 maths CBSE

Write a letter to the Principal of your school to plead class 10 english CBSE
