## Percentage

#### Percentage

1. In an examination 70% of the candidates passed in English. 80% passed in Mathematics. 10% failed in both the subjects. If 144 candidates passed in both, the total number of candidates were :

1. Let total number of candidates = 100
70 candidates passed in English and 30 failed in it.
80 candidates passed in Maths and 20 failed in it.
10 candidates failed in English and Maths both.
∴ Out of 30 failed in English, 10 failed in Maths also.
∴ 30 – 10 = 20 failed in English alone.
Similarly,
20 – 10 = 10 failed in Maths alone.
∴ Total number of failures
= 20 + 10 + 10 = 40
∴ 100 – 40 = 60 candidates passed in both subjects.
Now, if 60 candidates pass, total strength = 100
∴ For 144 candidates, total strength

 = 100 × 144 = 240 60

##### Correct Option: C

Let total number of candidates = 100
70 candidates passed in English and 30 failed in it.
80 candidates passed in Maths and 20 failed in it.
10 candidates failed in English and Maths both.
∴ Out of 30 failed in English, 10 failed in Maths also.
∴ 30 – 10 = 20 failed in English alone.
Similarly,
20 – 10 = 10 failed in Maths alone.
∴ Total number of failures
= 20 + 10 + 10 = 40
∴ 100 – 40 = 60 candidates passed in both subjects.
Now, if 60 candidates pass, total strength = 100
∴ For 144 candidates, total strength

 = 100 × 144 = 240 60

1. In a class 60% of the student pass in Hindi and 45% pass in Sanskrit. If 25% of them pass in at least one subject, what percentage of the students fail in both the subjects ?

1. 25% of students pass in at least one subject i.e.; they pass in one or both subjects.
∴ % of students who don’t pass or fail in both subjects
= (100 – 25)% = 75%

##### Correct Option: B

25% of students pass in at least one subject i.e.; they pass in one or both subjects.
∴ % of students who don’t pass or fail in both subjects
= (100 – 25)% = 75%

1. In an examination 60% of the students pass in English, 70% pass in Hindi and 40% pass in both. What percent of students fail in both English and Hindi?

1. The percentage of students who pass in one or two or both subjects
= 60 + 70 – 40 = 90
∴ Percentage of failed students
= 100 – 90 = 10%

##### Correct Option: A

The percentage of students who pass in one or two or both subjects
= 60 + 70 – 40 = 90
∴ Percentage of failed students
= 100 – 90 = 10%

1. In an examination 80% of the boys passed in English and 85% passed in Mathematics, while 75% passed in both. If 45 boys failed in both, the number of boys who sat for the examination was

1. Successful boys in English or Maths or both
= 80 + 85 – 75 = 90%
Unsuccessful boys = 10%
∴ Total number of boys

 = 100 × 45 = 450 10

##### Correct Option: B

Successful boys in English or Maths or both
= 80 + 85 – 75 = 90%
Unsuccessful boys = 10%
∴ Total number of boys

 = 100 × 45 = 450 10

1. A candidate who gets 20% marks in an examination fails by 30 marks but another candidate who gets 32% gets 42 marks more than the passing marks. Then the percentage of pass marks is :

1. Difference of percentages of maximum marks obtained by two
candidates = 32% – 20% = 12%
Difference of scores between two candidates = 30 +42 = 72
∴ 12% of maximum marks = 72
∴ Maximum marks

 = 72 × 100 = 600 12

∴ Pass marks = 20% of 600 + 30
= 120 + 30 = 150
∴ Required percentage
 = 150 × 100 = 25% 600

Aliter : Using Rule 22,
n = 32%, m=20%, p=30, q = 42.
 Full Marks = 100 × (p + q) n - m

 = 100 × (30 + 42) 32 - 20

 = 100 × 72 = 600 12

Pass marks =20% of 600 + 30
= 120 + 30 = 150
∴ Required percentage
 = 150 × 100 = 25% 600

##### Correct Option: D

Difference of percentages of maximum marks obtained by two
candidates = 32% – 20% = 12%
Difference of scores between two candidates = 30 +42 = 72
∴ 12% of maximum marks = 72
∴ Maximum marks

 = 72 × 100 = 600 12

∴ Pass marks = 20% of 600 + 30
= 120 + 30 = 150
∴ Required percentage
 = 150 × 100 = 25% 600

Aliter : Using Rule 22,
n = 32%, m=20%, p=30, q = 42.
 Full Marks = 100 × (p + q) n - m

 = 100 × (30 + 42) 32 - 20

 = 100 × 72 = 600 12

Pass marks =20% of 600 + 30
= 120 + 30 = 150
∴ Required percentage
 = 150 × 100 = 25% 600