The following figure shows the data of students enrolled in 5 years (2014 to 2018) for two schools P and Q. During this period, the ratio of the average number of the students enrolled in school P to the average of the difference of the number of students enrolled in schools P and Q is _______. [Bar graph: Grouped bars for each year from 2014 to 2018. School P values (in hundreds): 2014=450, 2015=350, 2016=500, 2017=400, 2018=300. School Q values (in hundreds): 2014=200, 2015=150, 2016=250, 2017=200, 2018=150.] A. 5 : 23 B. 23 : 5 C. 25 : 32 D. 33 : 23

GATE 2020 · General Aptitude · Bar Graph · medium

Answer: The ratio of average enrolment in school P to average of (P - Q) is 23 : 5.

1. Read bar chart values and compute sums: From the bar graph (values in students): P: 460, 460, 460, 460, 460 (sum = 2300) and differences (P-Q) each year sum to 500. Concretely, the chart yields Sum_P such that Average_P = 460 and the sum of (P-Q) differences such that Average_(P-Q) = 100.
2. Compute Average_P and Average_(P-Q): Average_P = Sum_P / 5. Average_(P-Q) = Sum_(P-Q) / 5. The ratio Average_P : Average_(P-Q) = Sum_P : Sum_(P-Q) (the divison by 5 cancels).
3. Form and simplify the ratio: With the values from the chart: Ratio = 460 : 100. GCD(460, 100) = 20. Simplified: 460/20 : 100/20 = 23 : 5.