Question

in an examination paper of 5 questions,5% answered all and 5% none. Of the rest 25% answered only 1 question, 20% answered 4 questions. If 24.5% of the whole answered 2 questions and 200 answered only 3 questions, how many candidates competed?”
720,680,980,800

Answer 1

.05x+.05x+.25(1-.10)x+.20(1-.10)x+.245x+200=x
.75x+200=x
x-.75x=200
.25x=200
x=800
The 1-.10 comes from the 25% and 20% of the remainder of the students after accounting for the first 10% that are excluded by the wording of the problem.

In other words only 25% of 90% answered 1 question, and 20% of 90% answered 4 questions