Question

Out of 1000 students who appeared for C.A. Intermediate Examination, 750 failed in Math, 600 failed in Accounts and 600 failed in Costing, 450 failed in both Math & Accounts, 400 failed in both Math & Costing, 150 failed in both Accounts & Costing. The Students who failed in all the three Subjects were 75. Prove that the above data is not correct.

Answer 1

Yes, the data provided is not correct. This can be proven using the principle of inclusion-exclusion.

According to the given data, the total number of students who failed in Math is 750, the total number of students who failed in Accounts is 600, and the total number of students who failed in Costing is 600.

However, if we apply the principle of inclusion-exclusion, the total number of students who failed in at least one of the three subjects should be equal to the sum of the number of students who failed in each subject, minus the number of students who failed in two subjects, plus the number of students who failed in all three subjects.

Therefore, using this principle, we have:

750 + 600 + 600 - 450 - 400 + 75 = 975

This result shows that the number of students who failed in at least one of the three subjects is 975, which is greater than the total number of students who appeared for the examination (1000), which is not possible.

Therefore, the given data is not correct.