Percentage — Case Study Based Questions

A teacher asked her students about their preferences for a school excursion. 45% students wanted to go to the amusement park, 15% to a zoo, 10% to a museum and the rest had no preference.

1. If 36 students wanted to go to the amusement park, then the total number of students is :
   (a) 70
   (b) 80
   (c) 75
   (d) 60

2. The number of students who preferred going to the zoo are :
   (a) 16
   (b) 10
   (c) 12
   (d) 14

3. The number of students who preferred going to the museum are :
   (a) 8
   (b) 7
   (c) 6
   (d) 10

4. The ratio of the number of students with no preference to those who wanted to go to an amusement park is :
   (a) 2 : 1
   (b) 1 : 2
   (c) 2 : 3
   (d) 1 : 4

Answer

1. Let the total number of students be x.

45% of x = 36

$\Rightarrow \dfrac{45}{100} \times x = 36\\[1em] \Rightarrow x = \dfrac{36 \times 100}{45}\\[1em] \Rightarrow x = \dfrac{3600}{45}\\[1em] \Rightarrow x = 80$

Hence, option (b) is the correct option.

2. Total number of students = 80.

Number of students who preferred going to the zoo = 15% of 80.

$= \dfrac{15}{100} \times 80\\[1em] = \dfrac{1200}{100}\\[1em] = 12$

Hence, option (c) is the correct option.

3. Total number of students = 80.

Number of students who preferred going to the museum = 10% of 80

$= \dfrac{10}{100} \times 80\\[1em] = \dfrac{800}{100}\\[1em] = 8$

Hence, option (a) is the correct option.

4. Percentage of students with no preference = [100 − (45 + 15 + 10)]% = (100 − 70)% = 30%.

Percentage of students who wanted to go to the amusement park = 45%.

Required ratio = 30% : 45%

$= \dfrac{30}{45}$

$= \dfrac{2}{3}$

= 2 : 3

Hence, option (c) is the correct option.

In his end-term examination, Rohan scored 54 out of 75 in English, 51 out of 75 in Hindi, 64 out of 80 in Mathematics and 60 out of 80 in Science.

1. What is the percentage of marks scored by him in English ?
   (a) 72%
   (b) 60%
   (c) 80%
   (d) 75%

2. What is the percentage of marks scored by him in Science ?
   (a) 70%
   (b) 80%
   (c) 75%
   (d) 72%

3. In which subject did he perform the best ?
   (a) English
   (b) Science
   (c) Hindi
   (d) Mathematics

4. In which subject did he perform the worst ?
   (a) Mathematics
   (b) Hindi
   (c) English
   (d) Science

Answer

1. Percentage of marks in English = $\left(\dfrac{54}{75} \times 100\right)$%

$= \dfrac{5400}{75}$%

= 72%

Hence, option (a) is the correct option.

2. Percentage of marks in Science = $\left(\dfrac{60}{80} \times 100\right)$%

$= \dfrac{6000}{80}$%

= 75%

Hence, option (c) is the correct option.

3. Percentage of marks in English = $\left(\dfrac{54}{75} \times 100\right)$% = 72%

Percentage of marks in Hindi = $\left(\dfrac{51}{75} \times 100\right)$% = 68%

Percentage of marks in Mathematics = $\left(\dfrac{64}{80} \times 100\right)$% = 80%

Percentage of marks in Science = $\left(\dfrac{60}{80} \times 100\right)$% = 75%

Since 80% is the highest percentage, Rohan performed the best in Mathematics.

Hence, option (d) is the correct option.

4. Percentage of marks in English = 72%, Hindi = 68%, Mathematics = 80% and Science = 75%.

Since 68% is the lowest percentage, Rohan performed the worst in Hindi.

Hence, option (b) is the correct option.