Directions : The students of a class are offered three languages (Hind...
Given information:
- 15 students learn all three languages.
- 28 students do not learn any language.
- 23 students learn only Hindi.
- 17 students learn only English.
- The total number of students learning French is 46 and the total number of students learning only French is 11.
To find out how many students learn precisely two languages, we need to first find out the number of students who learn only two languages.
Let's assume the number of students learning:
- Only Hindi and English but not French = x
- Only Hindi and French but not English = y
- Only English and French but not Hindi = z
Using the given information, we can create the following equations:
- x = 2y
- z = 3y
- (23-15-y-x) + (17-15-x-y) + (46-15-y-z) + 11 + x + y + z + 15 + 28 = total number of students in the class
- Simplifying the above equation, we get:
- 32 + 2x + 2y + 2z = total number of students in the class
- Substituting the values of x and z from the first two equations, we get:
- x = 2y
- z = 3y
- Therefore, x + y + z = 6y
- Simplifying the equation, we get:
- 32 + 8y = total number of students in the class
- Subtracting the number of students who do not learn any language, we get:
- 4y + 15 = total number of students who learn one or more languages
Now, we need to find the value of y to get the number of students who learn only two languages:
- From the equation x = 2y, we know that x is equal to 2 times y.
- From the equation z = 3y, we know that z is equal to 3 times y.
- Adding all the values, we get:
- x + y + z = 2y + y + 3y = 6y
- Therefore, the total number of students who learn only two languages is:
- x + y + z = 6y = 4y + 15 (from above equation)
- Solving the equation, we get y = 5
- Substituting the value of y in the equations for x and z, we get:
- x = 2y = 10
- z = 3y = 15
- Therefore, the number of students who learn precisely two languages is:
- x + y + z = 10 + 5 + 15 = 30
Hence, the correct answer is option (c) 30.
Directions : The students of a class are offered three languages (Hind...