Percentage
- 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 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%
- In a test a student got 30% marks and failed by 25 marks. In the same test another student got 40% marks and secured 25 marks more than the essential minimum pass marks. The maximum marks for the test were
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Let the maximum marks in the examination = x.
According to the question,= 40x - 30x = 50 100 100 = 10x = 50 100 ⇒ x = 50 × 100 = 500 10
Aliter : Using Rule 22,
m = 30%, n = 40%, p = 25 and q = 25
∴ Maximum marks= 100 × (p + q) (n - m) = 100 × (25 + 25) = 500 (40 - 30) Correct Option: C
Let the maximum marks in the examination = x.
According to the question,= 40x - 30x = 50 100 100 = 10x = 50 100 ⇒ x = 50 × 100 = 500 10
Aliter : Using Rule 22,
m = 30%, n = 40%, p = 25 and q = 25
∴ Maximum marks= 100 × (p + q) (n - m) = 100 × (25 + 25) = 500 (40 - 30)
- A candidate who scores 30 percent fails by 5 marks, while another candidate who scores 40 per cent marks gets 10 more than minimum pass marks. The minimum marks required to pass are
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Let the full marks in that examination were x.
According to the question,= 30x + 5 = 40x - 10 100 100 = 3x - 4x = 10 + 5 10 10 ⇒ x = 15 10
∴ x = 150
∴ Minimum pass marks⇒ 30 × 150 + 5 = 50 100
Aliter : Using Rule 22,
m = 30%, n = 40%,
p = 5, q = 10.
Maximum marks= 100 × (p + q) (n - m) = 100 × (5 + 10) = 150 (40 - 30)
∴ Minimum passing marks= 150 × 30 + 5 = 45 + 5 = 50 100 Correct Option: A
Let the full marks in that examination were x.
According to the question,= 30x + 5 = 40x - 10 100 100 = 3x - 4x = 10 + 5 10 10 ⇒ x = 15 10
∴ x = 150
∴ Minimum pass marks⇒ 30 × 150 + 5 = 50 100
Aliter : Using Rule 22,
m = 30%, n = 40%,
p = 5, q = 10.
Maximum marks= 100 × (p + q) (n - m) = 100 × (5 + 10) = 150 (40 - 30)
∴ Minimum passing marks= 150 × 30 + 5 = 45 + 5 = 50 100
- In an examination, 60% of the candidates passed in English and 70% of the candidates passed in Mathematics, but 20% failed in both of these subjects. If 2500 candidates passed in both the subjects, the number of candidates who appeared at the examination was
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Let the total number of candidates = x
∴ Number of candidates passed in English = 0.6x
Number of candidates passed in Maths = 0.7x
Number of candidates failed in both subjects = 0.2x
Number of candidates passed in at least one subject
= x – 0.2x = 0.8x
∴ 0.6 x + 0.7x – 2500 = 0.8 x
⇒ 1.3x – 0.8x = 2500
⇒ 0.5x = 2500⇒ x = 2500 = 5000 0.5 Correct Option: D
Let the total number of candidates = x
∴ Number of candidates passed in English = 0.6x
Number of candidates passed in Maths = 0.7x
Number of candidates failed in both subjects = 0.2x
Number of candidates passed in at least one subject
= x – 0.2x = 0.8x
∴ 0.6 x + 0.7x – 2500 = 0.8 x
⇒ 1.3x – 0.8x = 2500
⇒ 0.5x = 2500⇒ x = 2500 = 5000 0.5
