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?
- 1/24
- 1/12
- 1/4
- 5/6
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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