There are 50 students admitted to a nursery class. Some students can speak only English and some can speak only Hindi. Ten students can speak both English and Hindi. If the number of students who can speak English is 21, then how many students can speak Hindi, how many can speak only Hindi and how many can speak only English?

Options

A. 39, 29 and 11 respectively
B. 37, 27 and 13 respectively
C. 28, 18 and 22 respectively
D. 21, 11 and 29 respectively

Answer

A

Explanation

Let circles E and H represent the students who can speak English and Hindi respectively.

According to the question
Total number of students = a + b + c = 50 ... (i)
Number of students who can speak both English and Hindi = b = 10 ... (ii)
Number of students who can speak English
`= a + b = 21 ... (iii) `
So, Number of students who can speak only English
`=a = (a + b) - b `[From (ii) & (iii)]
`= 21 - 10 = 11 ... (iv) `
Number of students who can speak only Hindi
`= c = (a + b + c)-(a + b)`
`= 50 - 21 = 29 `
[From (i) & (iii)]
Number of students who can speak Hindi
`= b + c = 10 + 29 = 39 ` [From (ii) & (v)]
Therefore, required number of students who can speak Hindi, only Hindi and only English = 39, 29, 11, respectively.