Percentage
- In an examination, a student who gets 20% of the maximum marks fails by 5 marks. Another student who scores 30% of the maximum marks gets 20 marks more than the pass marks. The necessary percentage required for passing is :
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Let the maximum marks be x.
According to question,
20% of x + 5 = 30% of x –20
⇒ (30 –20)% of x = 25⇒ x = 25 × 100 = 250 10
∴ Passing marks
= 20% of 250 + 5 = 55
∴ % Passing marks= 55 × 100 = 22% 250
Aliter : Using Rule 22,
Here, m = 30%, n = 20%, p = 5 and q = 20
∴ Maximum marks= 100 × (p + q) (n - m) = 100 × (5 + 20) (30 - 20) = 100 × 25 = 250 10
Passing marks
= 20% of 250 + 5 = 55
∴ % of passing marks= 55 × 100 = 22% 250 Correct Option: C
Let the maximum marks be x.
According to question,
20% of x + 5 = 30% of x –20
⇒ (30 –20)% of x = 25⇒ x = 25 × 100 = 250 10
∴ Passing marks
= 20% of 250 + 5 = 55
∴ % Passing marks= 55 × 100 = 22% 250
Aliter : Using Rule 22,
Here, m = 30%, n = 20%, p = 5 and q = 20
∴ Maximum marks= 100 × (p + q) (n - m) = 100 × (5 + 20) (30 - 20) = 100 × 25 = 250 10
Passing marks
= 20% of 250 + 5 = 55
∴ % of passing marks= 55 × 100 = 22% 250
- In an examination, there were 1000 boys and 800 girls. 60% of the boys and 50% of the girls passed. Find the percent of the candidates failed ?
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Total candidates
= 1000 + 800 = 1800
The candidates who are passed= 100 × 60 + 800 × 50 % 100 100
= 600 + 400 = 1000
The number of candidates who failed = 1800 – 1000 = 800
∴ Required percent= 800 × 100 = 44.4% 1800
Aliter : Using Rule 25,
Percentage of passed students= B.b + G.g % B + G = 1000 × 60 + 800 × 50 1000 + 800 = 60000 + 40000 1800 = 100000 1800 = 500 = 55.5 9
∴ Percentage of failed students
= 100 – 55.5 = 44.4%Correct Option: C
Total candidates
= 1000 + 800 = 1800
The candidates who are passed= 100 × 60 + 800 × 50 % 100 100
= 600 + 400 = 1000
The number of candidates who failed = 1800 – 1000 = 800
∴ Required percent= 800 × 100 = 44.4% 1800
Aliter : Using Rule 25,
Percentage of passed students= B.b + G.g % B + G = 1000 × 60 + 800 × 50 1000 + 800 = 60000 + 40000 1800 = 100000 1800 = 500 = 55.5 9
∴ Percentage of failed students
= 100 – 55.5 = 44.4%
- If the price of petrol be raised by 20%, then the percentage by which a car owner must reduce his consumption so as not to increase his expenditure on petrol is
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Using Rule 8,
Percentage decrease in the consumption of petrol= 20 × 100 % 100 + 20 = 50 = 16 2 % 3 3 Correct Option: B
Using Rule 8,
Percentage decrease in the consumption of petrol= 20 × 100 % 100 + 20 = 50 = 16 2 % 3 3
- The price of petrol is increased by 25%. By how much per cent a car owner should reduce his consumption of petrol so that the expenditure on petrol would not be increased ?
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Using Rule 8,
Required percent= 25 × 100 = 20% 125 Correct Option: D
Using Rule 8,
Required percent= 25 × 100 = 20% 125
- Price of a commodity has increased by 60%. By what percent must a consumer reduce the consumption of the commodity so as not to increase the expenditure ?
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If the reduction in consumption be x%, then
60 - x - 60x = 0 100 ⇒ 60 - x - 3x = 0 5
⇒ 300 - 5x - 3x = 0
⇒ 8x = 300⇒ x = 300 = 37.5% 8
Aliter : Using Rule 8,
Required percentage= 60 × 100% 160 = 300 = 75 = 37.5% 8 2 Correct Option: B
If the reduction in consumption be x%, then
60 - x - 60x = 0 100 ⇒ 60 - x - 3x = 0 5
⇒ 300 - 5x - 3x = 0
⇒ 8x = 300⇒ x = 300 = 37.5% 8
Aliter : Using Rule 8,
Required percentage= 60 × 100% 160 = 300 = 75 = 37.5% 8 2