Dear Reader, questions on averages can be expected on Capgemini papers. Below are few questions with solutions for your practice.

Question 1

Ashwin Kumar scored 32 marks in Geography, 29 marks in History, 40 marks in Science, 36 marks in mathematics , 33 marks in English and 35 marks in Hindi. Consider that pass mark is same across all subjects. Also assume that college hasn't declared a pass mark before the exams are conducted. Now, the college administration sets a maximum pass mark that would take care that Ashwin Kumar JUST PASSES. Considering all the subjects, by what percentage Ashwin Kumar would have exceeded the pass marks ?

a) 15% b) 33.3% c) 17.8% d) 19.7%

Answer : c) 17.8%

Solution :

For Ashwin to just pass in all subjects, the minimum pass mark should be 29 (which is his lowest score.)

The average mark of Ashwin = His Total Marks / No of subjects
= 32+29+40+36+33+35 / 6 = 205/6

Average mark of Ashwin exceeds the pass percentage by = (Ashwin's Average - Minimum Pass Mark ) / Minimum Pass Mark x 100 %
= (205/6 - 29)/29 x 100

= 31/174 * 100
= 17.8% (approximately)

Question 2

Average age of total 80 students from three classes V, VI and VII is 13 years. Average age of 30 students of class V is 11 1/2 years. If average age of another 30 students of class VI is 12 1/2 years, what is the average of the rest of the students who are in class VII?

a) 13 b) 14 c) 16 d) 15

Answer : c) 16

Solution :

Sum of ages of all the 80 students = 80 x 13 = 1040
Sum of ages of 30 students of class V = 30 x 11.5 = 345
Sum of ages of 30 students of class VI = 30 x 12.5 = 375
Total age of rest of the students (20) of class VII = 1040 – (345 + 375) = 320
Average age of these 20 students = 320/20 = 16

Question 3

Assume a project team of 4 students. The project guide (their professor) had estimated that every one of the students would take approximately 200 working hours to complete the project. But, the first two students lagged by 20 hours each while the last two students completed their tasks 10 hours each in advance. By what percentage is the actual working hours exceeds the actual estimate ?

a) 2.5% b) 5% c) 4% d) 8.5%

Answer : a) 2.5%

Solution :

Estimated Total Hours to complete the project = Working Hours Estimate Per Student x No of Students = 200 x 4 = 800.

Case I : Consider first two students.

They lagged by 20 hours each. This means each took 220 hours to complete their tasks.

Actual hours of work by first two students = actual working hours per student x no of students = 220 x 2 = 440.

Case II : Consider last two students.

They completed in advance by 10 hours each. This means each took 190 hours to complete their tasks.

Actual hours of work by last two students = actual working hours per student x no of students = 190 x 2 = 380.

Conclusion :

Actual Total Working hours of all 4 students = Working hours of first 2 students + Working hours of last 2 students = 440 + 380 = 820 hours.

Percentage increase in actual working hours compared to estimate = (Actual total working hours - Estimated total working hours) / Estimated total working hours x 100%

= ((820 - 800) / 800) x 100
= 2000/800 %
= 2.5%