Instructions

In a College P there are 19,000 students. They know different languages like Japanese. Korean and Latin. Ratio of males and females is 9 : 11. 14% of males know only Japanese. 12% know only Korean. 20% know only Latin. 16% know only Korean and Japanese. 22% know only Korean and Latin. 8% know only Japanese and Latin. Remaining boys know all the languages. 22% females know only Japanese. 18% know only Korean. 20% know only Latin. 12% know only  Japanese and Korean. 16% know only Korean and Latin. 10% know only Japanese and Latin. Remaining females know all the languages.

Question 160

# How many females know at least two languages?

Solution

Total students in college P = 19000

Total males = $$\frac{9}{20} \times 19000 = 8550$$

=> Females = $$19000 - 8550 = 10450$$

Males who know all the three languages = 100 - (14+16+12+8+22+20) = 8%

Similarly, females who knows who all three languages = 2%

Numbers given in the venn diagram are percentages.

% of females know at least two languages = (12 + 10 + 16 + 2)% = 40%

=> Number of females know at least two languages = $$\frac{40}{100} \times 10450$$

= 4180