Question

In a class, 70% student can speak English, 65% can speak Hindi and 27% can speak neither English nor Hindi. If 124 students can speak both languages then find the no. of students who can speak only Hindi. (A) 6 (B) 8 (C) 10 (D) 24

Answer 1

SOLUTION

TO CHOOSE THE CORRECT OPTION

In a class, 70% student can speak English, 65% can speak Hindi and 27% can speak neither English nor Hindi. If 124 students can speak both languages then the no. of students who can speak only Hindi.

(A) 6

(B) 8

(C) 10

(D) 24

EVALUATION

Let total number of students = 100x

Let

E : The set of students who can speak English

H : The set of students who can speak Hindi

By the given condition

n(E) = 70x , n(H) = 65x

Now 27% can speak neither English nor Hindi

So ( 100 - 27) % = 73% can speak atleast one of English or Hindi

n(E ∪ H) = 73x

Now

n(E ∪ H) = n(E) + n(H) - n(E ∩ H)

⇒ 73x = 70x + 65x - n(E ∩ H)

⇒ n(E ∩ H) = 135x - 73x

⇒ n(E ∩ H) = 62x

By the given condition

62x = 124

⇒ x = 2

The number of students who can speak only Hindi

= E(H) - n(E ∩ H)

= 65x - 62x

= 3x

= 3 × 2

= 6

FINAL ANSWER

Hence the correct option is (A) 6

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Answer 2

From the given question the correct option is (A) 6.

Solution :

Let total number of students = 100x

Let

E : The set of students who can speak English

H : The set of students who can speak Hindi

By the given condition

n(E) = 70x , n(H) = 65x

Now 27% can speak neither English nor Hindi

So ( 100 - 27) % = 73% can speak atleast one of English or Hindi

n(E ∪ H) = 73x

Now

n(E ∪ H) = n(E) + n(H) - n(E ∩ H)

⇒ 73x = 70x + 65x - n(E ∩ H)

⇒ n(E ∩ H) = 135x - 73x

⇒ n(E ∩ H) = 62x

By the given condition

62x = 124

⇒ x = 2

The number of students who can speak only Hindi

= E(H) - n(E ∩ H)

= 65x - 62x

= 3x

= 3 × 2

= 6

FINAL ANSWER

Hence the correct option is (A) 6