Dear Reader,
Below are 3 easy problems where one has to calculate percentages.

Question 1

Sri Kamala Meenakshi Sundaram Engineering conducted an aptitude test for its students.90% of the boys and 30% of the girls passed the test. The number of boys was 40% of total number of students who took the test. What is the percentage of boys who have passed as against total number of students who have passed the test?

a) 88.88 b) 77.77 c) 66.66 d) 33.33

Answer : c) 66.66

Solution :

Percentage of boys to total students --- 40% of the students
Percentage of boys who passed the test -- 90% of the boys = 90% of 40% of the students = 36% of the students
Balance students – girls -- 60% of the students
Percentage of girls who passed the test - 30% of the girls = 30% of 60% of the students = 18% of the students
Total percentage of students who passed the test 36 + 18 = 54%
In other words, if there were 54 students then 36 boys would had passed.

Students            Passed Boys
54                     36
100                    ?

Percentage of boys who passed the test as against total number of students who passed the test = 36/54 x 100 = 66.66%

Question 2

Vijayasooriyan Televisions a serial producing company conducted a contest to decide the best actor of one of their TV serials. Viewers were permitted to send the answers/responses through email or SMS. 80% of answers received through email and 75% of answers received through SMS were correct. Answers received through email constituted 70% of total responses(answers) received. What is the percentage of correct answers received through email to total number of answers received through both modes?

a) 71.33 b) 62.43 c) 88.34 d) 23.35

Answer : a) 71.33

Solution :

Percentage of responses / answers received through email - 70%
Percentage of responses / answers received through SMS - 30%
Correct Answers received through email - 80% of 70% of all responses = 80/100 x 70 = 56% of all responses
Correct answers received through SMS = 75% of 30% of all responses = 75/100 x 30 = 22.5% of all responses
Correct answers received through both modes = 56 + 22.5 = 78.5%

Correct Answers                      Correct Answers Through Email
78.5                                         56
100                                           ?

Percentage of correct answers received through email as compared to total correct answers received through both modes = 56/78.5 x 100 = 71.33%

Question 3

Nilgiris Restaurant wanted to improve its turnover and conducted a “dosa mela” from 15th July to 22nd July 2012. On these days customers were provided with varieties of dosa on Buffet system and through Table service system. Charges for Table service was 20% more than what is charged for buffet system.
On 22nd July 2012-- 60% of those who opted for buffet and 25% of those who opted for Table service rated the food as Excellent . 70% of customers opted for buffet on 22nd July,2012. What is the percentage of Table service customers rated Excellent as against the total percentage of customers who rated Excellent under both systems?. (Buffet and Table service)

a) 15.15 b) 84.85 c) 72.35 d) none of these.

Answer : a) 15.15%

Solution :

Percentage of customers opted for buffet -- 70%
Percentage of customers opted for table service -- 30%
Percentage of buffet customers who rated the service to be excellent - 60% of 70% of customers = 60/100 x 70 = 42%
Percentage of table service customers who rated the service to be excellent – 25% of 30% of customers = 25/100x30 = 7.5%
Total percentage of customers who gave Excellent rating (both modes) = 42%+ 7.5% = 49.5%

Table Service Customers                              Total Customers 
Who Rated Excellent                                  Who Rated Excellent
7.5                                                      49.5
?                                                         100

Percentage of table service customers rated Excellent to Total percentage of customers rating as Excellent(both modes) = 7.5/49.5 x 100 = 15.15%