In a class of 150 students 55 speak English, 85 speak Telugu and 30 speak neither English nor Telugu. How many speak both English & Telugu?a.10b.120c.20d.45
Question
In a class of 150 students, 55 speak English, 85 speak Telugu, and 30 speak neither English nor Telugu.
How many speak both English & Telugu?
a. 10
b. 120
c. 20
d. 45
Solution
The problem can be solved using the principle of inclusion and exclusion.
Step 1: Find the total number of students who speak at least one language. This is the total number of students minus the number who speak neither language. So, 150 - 30 = 120 students speak either English or Telugu.
Step 2: Find the total number of students who speak English or Telugu. This is the sum of the number of students who speak English and the number of students who speak Telugu. So, 55 + 85 = 140.
Step 3: The number of students who speak both languages is the total from step 2 minus the total from step 1. So, 140 - 120 = 20.
So, the answer is c. 20.
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