Percentage
- In a quarterly examination a student secured 30% marks and failed by 12 marks. In the same examination another student secured 40% marks and got 28 marks more than minimum marks to pass. The maximum marks in the examination is
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Maximum marks in the examination = x (let)
= 40x - 30x = 12 + 28 100 100 = 10x = 40 ⇒ x = 40 × 10 = 400 100
Aliter : Using Rule 22,
Here, m = 30%, n = 40%, p = 12, q = 28
∴ Maximum marks= 100 × (p + q) (n - m) = 100 × (12 + 28) (40 - 30) = 100 × 40 = 400 10 Correct Option: D
Maximum marks in the examination = x (let)
= 40x - 30x = 12 + 28 100 100 = 10x = 40 ⇒ x = 40 × 10 = 400 100
Aliter : Using Rule 22,
Here, m = 30%, n = 40%, p = 12, q = 28
∴ Maximum marks= 100 × (p + q) (n - m) = 100 × (12 + 28) (40 - 30) = 100 × 40 = 400 10
- In an examination there are three subjects of 100 marks each. A student scores 60% in the first subject and 80% in the second subject. He scored 70% in aggregate. His percentage of marks in the third subject is
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Total marks scored in all three subjects
= 300 × 70 = 210 100
∴ Marks scored in third subject
= 210 – 60 – 80 = 70Correct Option: D
Total marks scored in all three subjects
= 300 × 70 = 210 100
∴ Marks scored in third subject
= 210 – 60 – 80 = 70
- In an examination, a student must get 36% marks to pass. A student who gets 190 marks failed by 35 marks. The total marks in that examination is
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Let total marks in the exam be x.
According to the question,= x × 36 = 190 + 35 = 225 100
⇒ x × 36 = 225 × 100⇒ x = 225 × 100 = 625 36
Aliter : Using Rule 24,
a = 36%, b = 190, c = 35Total marks = (b + c) × 100 a = (190 + 35) × 100 36 = 225 × 100 = 625 36 Correct Option: D
Let total marks in the exam be x.
According to the question,= x × 36 = 190 + 35 = 225 100
⇒ x × 36 = 225 × 100⇒ x = 225 × 100 = 625 36
Aliter : Using Rule 24,
a = 36%, b = 190, c = 35Total marks = (b + c) × 100 a = (190 + 35) × 100 36 = 225 × 100 = 625 36
- A candidate who gest 20% marks in an examination, fails by 30 marks. But if he gets 32% marks, he gets 42 marks more than the minimum pass marks. Find the pass percentage of marks.
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Let the full marks of exam be x.
According to the question,= x × 32 - x × 20 = 30 + 42 100 100 = 12x = 72 100 ⇒ x = 72 × 100 = 600 12
∴ Minimum marks to pass⇒ x = 600 × 20 + 30 = 120 + 30 = 150 100
∴ Required percentage= 150 × 100 = 25% 600
Aliter : Using Rule 22,
Here, m = 20%, n = 32%, p = 30 and q = 42Full Marks = 100 × (p + q) (n - m) = 100 × (30 + 42) (32 - 20) = 100 × 72 = 600 12
∴ Passing Marks = 20% of 600 + 30= 20 × 600 + 30 = 120 + 30 = 150 100 ∴ Pass percentage = 150 × 100 = 25% 600 Correct Option: C
Let the full marks of exam be x.
According to the question,= x × 32 - x × 20 = 30 + 42 100 100 = 12x = 72 100 ⇒ x = 72 × 100 = 600 12
∴ Minimum marks to pass⇒ x = 600 × 20 + 30 = 120 + 30 = 150 100
∴ Required percentage= 150 × 100 = 25% 600
Aliter : Using Rule 22,
Here, m = 20%, n = 32%, p = 30 and q = 42Full Marks = 100 × (p + q) (n - m) = 100 × (30 + 42) (32 - 20) = 100 × 72 = 600 12
∴ Passing Marks = 20% of 600 + 30= 20 × 600 + 30 = 120 + 30 = 150 100 ∴ Pass percentage = 150 × 100 = 25% 600
- If the income tax is increased by 19%, the net income is reduced by 1%. The rate of income tax is
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Let the income be ₹x and the rate of income tax be y %
According to the question,xy × 1.19 - xy 100 100 = 
x - xy 
× 1 100 100 ⇒ 1.19 xy – xy = x - xy 100 ⇒ 1.19y = 1 - y 100 ⇒ y + 1.19y = 1 100 ⇒ y 1 + 19 = 1 100 ⇒ y = 100 = 5% 20 Correct Option: C
Let the income be ₹x and the rate of income tax be y %
According to the question,xy × 1.19 - xy 100 100 = x - xy × 1 100 100 ⇒ 1.19 xy – xy = x - xy 100 ⇒ 1.19y = 1 - y 100 ⇒ y + 1.19y = 1 100 ⇒ y 1 + 19 = 1 100 ⇒ y = 100 = 5% 20
