A student has 5 subjects in an examination. The distribution of hard work of 16 hours a day over 5 subjects and marks obtained 400 out of 500 are shown in the charts.

In which subject did the student get the highest outcome of the hard work (ratio of marks to hard work is highest)?

Correct option is A

​​​Given:

Total time devoted = 16 hours

Total marks scored = 400 out of 500

Solution:

Marks scored in English = $$\frac{20}{100}×400=80$$​​

Marks scored in Math =$$\frac{21}{100}×400=84$$​​

Marks scored in science = $$\frac{18}{100}×400=72$$​​

Marks scored in Economics = $$\frac{19}{100}×400=76$$​​

Marks scored in Sociology = $$\frac{22}{100}×400=88$$​​

Time given for English = $$\frac {5}{100}×16=\frac 45$$​​

Time given for Math = $$\frac{40}{100}×16=\frac{32}{5}$$​​

Time given for Science = $$\frac{20}{100}×16=\frac{16}{5}$$​​

Time given for Economics = $$\frac{10}{100}×16=\frac 85$$​​

Time given for Sociology = $$\frac {25}{100}×16=4$$​​

Ratio of marks and time taken in English = $$\frac {\frac {80}{1}}{\frac{4}{5}}=\frac{80×5}{4}=100:1$$​​

Ratio of marks and time taken in Math = $$\frac{\frac{84}{1}}{\frac{32}{5}} = \frac{84 \times 5}{32} = \frac{105}{8} = 13.125:1$$​​

Ratio of marks and time taken in science = $$\frac{\frac{72}{1}}{\frac{16}{5}} = \frac{72 \times 5}{16} = 22.5:1$$​​

Ratio of marks and time taken in Economics =$$\frac{\frac{76}{1}}{\frac{8}{5}} = \frac{76 \times 5}{8} = \frac{60}{1}$$​​

Ratio of marks and time taken in Sociology = $$\frac{88}{4} = 22:1$$​​

So, the ratio of marks and time taken in English is the highest one.