Percentage
- In an examination 34% failed in Mathematics and 42% failed in English. If 20% failed in both the subjects, the percentage of students who passed in both subjects was
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Let total number of students = 100
Number of failures in Maths = 34
Number of failures in English = 42
Number of failures in both subjects = 20
Number of failures in Maths or English or both
= 34 + 42 – 20 = 56
Number of students who passed in both subjects
= 100 – 56 = 44
The required percentage = 44%
Aliter : Using Rule 23,
a = 34%, b = 42%, c = 20%
Passed candidates in both the subjects
= 100 – (a + b – c)
= 100 – (34 + 42 – 20)
= 100 – 56 = 44%Correct Option: C
Let total number of students = 100
Number of failures in Maths = 34
Number of failures in English = 42
Number of failures in both subjects = 20
Number of failures in Maths or English or both
= 34 + 42 – 20 = 56
Number of students who passed in both subjects
= 100 – 56 = 44
The required percentage = 44%
Aliter : Using Rule 23,
a = 34%, b = 42%, c = 20%
Passed candidates in both the subjects
= 100 – (a + b – c)
= 100 – (34 + 42 – 20)
= 100 – 56 = 44%
- In an examination there were 640 boys and 360 girls. 60% of boys and 80% of girls were successful. The percentage of failure was :
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Total number of students = 640 + 360 = 1000
Number of successful boys = 60% of 640 = 384
Number of successful girls = 80% of 360 = 288
Total number of successful students = 384 + 288 = 672
Number of unsuccessful students = 1000 – 672 = 328
∴ Required percentage= 328 × 100 = 32.8% 1000
Aliter : Using Rule 25,
B = 640, G = 360,
b = 60%, g = 80%
Percentage of passed students= 
B.b + G.g 
% B + G = 640 × 60 + 360 × 80 640 + 360 = 38400 + 28800 1000 = 67200 = 67.2% 1000
∴ % of failed students
= 100 – 67.2% = 32.8%Correct Option: D
Total number of students = 640 + 360 = 1000
Number of successful boys = 60% of 640 = 384
Number of successful girls = 80% of 360 = 288
Total number of successful students = 384 + 288 = 672
Number of unsuccessful students = 1000 – 672 = 328
∴ Required percentage= 328 × 100 = 32.8% 1000
Aliter : Using Rule 25,
B = 640, G = 360,
b = 60%, g = 80%
Percentage of passed students= B.b + G.g % B + G = 640 × 60 + 360 × 80 640 + 360 = 38400 + 28800 1000 = 67200 = 67.2% 1000
∴ % of failed students
= 100 – 67.2% = 32.8%
- 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 :
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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
- 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 :
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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
- 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?
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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%
