Question

Read the information given in the passage and answer the given questions.
There are 19000 students in college P. Each of them is studying either one or more of the given languages Japanese, Korean and Latin. The ratio of male to female students is 9: 11. 14% of the male students study only Japanese, 12% study only Korean and 20% study only Latin. 16% of the male students study only Japanese and Korean, 22% study only Korean and Latin and 8% study only Japanese and Latin. The remaining male students study all the given languages. 22% of the female students study only Japanese, 18% study only Korean and 20% study only Latin. 12% of the female students study only Japanese and Korean, 16% study only Korean and Latin and 10% study only Japanese and Latin. The remaining female students study all the given languages.

What is the difference between the number of female students who study Latin and the number of male students who study the same language?

• A. 43
• B. 76
• C. 83
• D. 62
• E. 57

Answer 1

The correct option is E 57

Total number of students in college P = 19000
Ratio of male females students = 9 : 11
Male students $-\frac{19000}{20}\times 9=8550$
Female students $=\frac{11}{20}\times 19000$
= 10450
Number of male students who study only Japanese
$=\frac{14}{100}\times 8550=1197$
Number of male students who study only Korean
$=\frac{12\times 8550}{100}=1197$
Number of male students who study only Latin
$=\frac{20\times 8550}{100}=1710$
The number of male students who study only Japanese and Korean
$=\frac{16\times 8550}{100}=1368$
The number of male students who study only Korean and Latin
$=\frac{22\times 8550}{100}=1881$
Number of male students who study only Japanese and Latin
$=\frac{8\times 8550}{100}=684$
Number of male students who study all the three languages
$=8550-(1197+1026+1710+1368+1881+684)=8550-7866=684$
Similarly, the number of female students who study only Japanese
$=\frac{10450\times 22}{100}=2299$
The number of female students who study only Korean
$=\frac{18\times 10450}{100}=1881$
The number of female students who study only Latin
$=\frac{10450}{100}\times 20=2090$
The number of female students who study only Japanese and Korean
$=\frac{12\times 10450}{100}\times 20=1254$
The number of female students who study only Korean and Latin
$=\frac{16\times 10450}{100}=1672$
The number of female students who study only Japanese and Latin
$=\frac{10450\times 10}{100}=1045$
The number of female students who study all three languages
$=10450-(2299+1881+2090+1254+1672+1045)=10450-10241=209$


Required difference
= (2090 + 1045 + 209 + 1672)
- (684 + 1881 + 1710 + 684)
= 5016 - 4959 = 57