Question

18. In an examination, 53% students passed in
Mathematics, 61 % passed in Physics, 60%
passed in Chemistry, 24% passed in
Mathematics and Physics, 35% in Physics and
Chemistry, 27% in Mathematics and
Chemistry and 5% in none. The ratio of
percentage of passes in Mathematics and
Chemistry but not in Physics in relation to the
percentage of passes in Physics and
Chemistry but not in Mathematics is​

Answer 1

Step-by-step explanation:

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 20/28=5/8

hope my answer helped you!