Question

In an examination,53% students passed in maths,61% passrd in physics,60% passed in chemistry,24% passed in maths and physics,35% passed in physics and chemistry,27% passed in maths and chemistry and 5% in none. The ratio of percentage of passes in maths and chemistry but not in physics in relation to percentage of passes in physics and chemistry but not in maths is?

Answer 1

Solution:

Let M be the percentage of students who passed Math, M=53%

Let P be the percentage of students who passed Physics, P=61%

Let C be the percentage of students who passed Chemistry, C=60%

Let MP be the percentage of students who passed math and physics, MP=24%

Let PC be the percentage of students who passed physics and chemistry, PC=35%

Let MC be the percentage of students who passed math and chemistry, MC=27%

Let N be the percentage of students who passed none, N=5%

The only unknown term is intersection of three that is percentage those who have passed Math, Physics and Chemistry

From the elementary set theory we have:

100% =  N + M + P + C - MP - PC - MC + MPC

100% = 5% + 53% + 61% + 60% - 24% - 35% - 27% + MPC

100% = 93% +MPC

MPC = 100% - 93% = 7%

Now,  in the ratio, the numerator is  MC - MPC = 27% - 7% = 20%;

the denominator is  PC - MPC = 35% - 7% = 28%

Therefore, the ratio is equal to $\frac{20}{28}= \frac{5}{7}$