In a class 3/4 of the students do not know either Hindi or English. 1/6 of the students know English and 1/8 of the students know Hindi. What part of the students know both English and Hindi?

Explanation

1. 3/4 of the students do not know either Hindi or English.

This means that 1 - 3/4 = 1/4 of the students know either Hindi or English or both.

2. 1/6 of the students know English.

3. 1/8 of the students know Hindi.

Now, let's use the principle of inclusion-exclusion:

Number of students who know either Hindi or English or both = Number of students who know English + Number of students who know Hindi - Number of students who know both

We know that 1/4 of the students know either Hindi or English or both. We also know the number of students who know English (1/6) and the number of students who know Hindi (1/8).

Let x be the number of students who know both English and Hindi.

Then, we can set up the equation:

1/4 = 1/6 + 1/8 - x

Combine like terms:

1/4 = 7/24 - x

Add x to both sides:

x = 7/24 - 1/4

x = 7/24 - 6/24

x = 1/24

So, 1/24 of the students know both English and Hindi.

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