Question

In a school, 150 students offered Hindi as an optional subject, 85 French and 90 Sanskrit. Out of these, 73 offered Hindi only, 52 French only, 18 Hindi and French only and 10 French and Sanskrit only. How many students offered Sanskrit only?

• A. 28
• B. 21
• C. 19
• D. 11
• E. 5

Answer 1

The Correct Option is B

The correct answer is option (B):

21

Let's break down this problem using a Venn diagram approach. We have three subjects: Hindi, French, and Sanskrit. We're given a lot of information about the overlaps.

We know:

* Total Hindi students: 150
* Total French students: 85
* Total Sanskrit students: 90
* Hindi only: 73
* French only: 52
* Hindi and French only: 18
* French and Sanskrit only: 10

Let's use variables to represent the unknowns:

* Let 'x' be the number of students who offered Hindi and Sanskrit only.
* Let 'y' be the number of students who offered all three subjects (Hindi, French, and Sanskrit).
* Let 'z' be the number of students who offered Sanskrit only. This is what we want to find.

Now, we can set up equations based on the information we have.

Focusing on Hindi students:

* Hindi only + Hindi and French only + Hindi and Sanskrit only + all three = Total Hindi
* 73 + 18 + x + y = 150
* x + y = 150 - 73 - 18
* x + y = 59 (Equation 1)

Focusing on French students:

* French only + Hindi and French only + French and Sanskrit only + all three = Total French
* 52 + 18 + 10 + y = 85
* y = 85 - 52 - 18 - 10
* y = 5 (We now know the number of students who took all three subjects!)

Substitute y = 5 into Equation 1:

* x + 5 = 59
* x = 59 - 5
* x = 54 (Now we know the number of students who took Hindi and Sanskrit only)

Focusing on Sanskrit students:

* Sanskrit only + Hindi and Sanskrit only + French and Sanskrit only + all three = Total Sanskrit
* z + x + 10 + y = 90
* z + 54 + 10 + 5 = 90 (Substitute the known values)
* z + 69 = 90
* z = 90 - 69
* z = 21

Therefore, 21 students offered Sanskrit only.