In a class, daily three subjects A, B, and C are read. 21% of the students read subject A, 27% of the students read B and 34% read C. 15% of the students read A and B, 14% of students read B and C, 13% read A and C, 5% do not read any of the three subjects, the percentage of students who read all the three subjects is:

We are asked to find the percentage of students who read all three subjects (A, B, and C).

The formula for the union of three sets is:

∣A∪B∪C∣=∣A∣+∣B∣+∣C∣−∣A∩B∣−∣B∩C∣−∣A∩C∣+∣A∩B∩C∣

∣A∣=21%, ∣B∣=27%, ∣C∣=34% ∣A∩B∣=15%, ∣B∩C∣=14%, ∣A∩C∣=13% and 5% of students don't read any of the three subjects, so

∣A∪B∪C∣=95%.

Substituting these values into the inclusion-exclusion formula:

95 = 21 + 27 + 34 − 15 − 14 − 13 +∣A∩B∩C∣

∣A∩B∩C∣= 95 −  40 = 55%