In a class, 40 students passed in Mathematics, 50% of the students passed in English, 5% of the students failed in Mathematics and English, and 25% of the students passed in both the subjects. What is the ratio of the number of students who passed in English to that in Mathematics?<\/p>\n
[amp_mcq option1=”1 : 1″ option2=”2 : 3″ option3=”5 : 7″ option4=”10 : 9″ correct=”option3″]<\/p>\n
Let P(M) be the set of students who passed in Mathematics, and P(E) be the set of students who passed in English.
\nWe are given:
\n|P(M \u2229 E)| \/ S = 0.25
\n|P(E)| \/ S = 0.50
\n|P(M \u222a E)| \/ S = 1 – 0.05 = 0.95<\/p>\n
Using the principle of inclusion-exclusion for percentages:
\n|P(M \u222a E)| \/ S = |P(M)| \/ S + |P(E)| \/ S – |P(M \u2229 E)| \/ S
\n0.95 = |P(M)| \/ S + 0.50 – 0.25
\n0.95 = |P(M)| \/ S + 0.25
\n|P(M)| \/ S = 0.95 – 0.25 = 0.70
\nSo, 70% of the total students passed in Mathematics.<\/p>\n
We are given that the number of students who passed in Mathematics is 40.
\n|P(M)| = 40.
\nTherefore, 70% of S = 40.
\n0.70 * S = 40
\nS = 40 \/ 0.70 = 400 \/ 7.<\/p>\n
Number of students who passed in English = |P(E)| = 50% of S = 0.50 * S.
\n|P(E)| = 0.50 * (400 \/ 7) = 0.5 * 400 \/ 7 = 200 \/ 7.<\/p>\n