There was an examination in class in which there were two questions asked. If 75% of the students were able to answer the first question correctly, 55% were able to answer the second question correctly and 20% answered both the questions wrong.

What percentage of students answered both the questions correctly?

Can anyone explain me with solution?


Hi. This is an easy question. Can be solved using a Venn diagram for ease of illustration. The total possible percentage of those who could answer both questions cannot exceed 80% because 20% clearly got both questions wrong. Now within that remaining 80% you have 75% who got the first question right, and some 55% who got the second question right. Total would 75 + 55 = 130 who either got the first or second question right. However, the total should not exceed 80%, therefore, the total of 130 should include those who got both questions right and therefore are being DOUBLE COUNTED in both groups. Just deduct 80 from 130 AND (130 - 80 = 50) you will have the answer = 50%. 50% of the total students got both questions RIGHT. You are welcome :slight_smile: