Percentage
- In an examination A got 25% marks more than B, B got 10% less than C and C got 25% more than D. If D got 320 marks out of 500, the marks obtained by A were
-
View Hint View Answer Discuss in Forum
If D gets 100 marks, then
Marks obtained by C = 125
Marks obtained by B= 125 × 90 100
Marks obtained by A= 125 × 90 × 125 100 100 ∵ 100 = 125 × 125 × 90 10000 ∴ 320 = 125 × 125 × 90 × 320 = 450 1000000 Correct Option: B
If D gets 100 marks, then
Marks obtained by C = 125
Marks obtained by B= 125 × 90 100
Marks obtained by A= 125 × 90 × 125 100 100 ∵ 100 = 125 × 125 × 90 10000 ∴ 320 = 125 × 125 × 90 × 320 = 450 1000000
- In two successive years, 80 and 60 students of a school appeared at the final examination of which 60% and 80% passed respectively. The average rate of students passed (in percent) is
-
View Hint View Answer Discuss in Forum
Total examiners = 80 + 60 = 140
Total successful examiners= 80 × 60 + 60 × 80 100 100
= 48 + 48 = 96.
∴ Required percent= 96 × 100 140 = 480 = 68 4 % 7 7
Aliter : Using Rule 25,
Let us take B = 80, G = 60 and b = 60%, g = 80%
∴ Percentage of passed candidates= 
B.b + G.g 
% B + G = 80 × 60 + 60 × 80 % 80 + 60 = 9600 140 = 480 = 68 4 % 7 7 Correct Option: B
Total examiners = 80 + 60 = 140
Total successful examiners= 80 × 60 + 60 × 80 100 100
= 48 + 48 = 96.
∴ Required percent= 96 × 100 140 = 480 = 68 4 % 7 7
Aliter : Using Rule 25,
Let us take B = 80, G = 60 and b = 60%, g = 80%
∴ Percentage of passed candidates= B.b + G.g % B + G = 80 × 60 + 60 × 80 % 80 + 60 = 9600 140 = 480 = 68 4 % 7 7
- In an examination, 19% students fail in Mathematics and 10% students fail in English. If 7% of all students fail in both subjects, then the number of students passed in both subjects is
-
View Hint View Answer Discuss in Forum
n (A ∪ B)
= n(A) + n(B) – n (A ∩ B)
= 19 + 10 – 7 = 22%
i.e. 22% of students are unsuccessful in either one or two subjects.
∴ Percentage of successful students = 100 – 22 = 78%
Aliter : Using Rule 24,
a = 19%, b = 10%, c = 7%
Passed students in both the subjects
= 100 – (a + b – c)
= 100 – (19 + 10 – 7)
= 100 – 22 = 78%Correct Option: D
n (A ∪ B)
= n(A) + n(B) – n (A ∩ B)
= 19 + 10 – 7 = 22%
i.e. 22% of students are unsuccessful in either one or two subjects.
∴ Percentage of successful students = 100 – 22 = 78%
Aliter : Using Rule 24,
a = 19%, b = 10%, c = 7%
Passed students in both the subjects
= 100 – (a + b – c)
= 100 – (19 + 10 – 7)
= 100 – 22 = 78%
- A class has two sections, which contain 20 and 30 students. The pass percentage of these sections are 80% and 60% respectively. The pass percentage of whole class is
-
View Hint View Answer Discuss in Forum
Successful students in both classes
= 20 × 80 + 30 × 60 = 16 + 18 = 34 100 100
∴ Required percentage= 34 × 100 = 68% 50
Or
Required percentage= 20 × 80 + 30 × 60 50 = 1600 + 1800 + 3400 = 68% 50 50
Aliter : Using Rule 25,
Let us take B = 20, G = 30, b = 80%, g = 60%
∴ Required percentage= Bb+ Gg B + G = 20 × 80 + 30 × 60 % 20 + 30 = 3400 = 68% 50 Correct Option: B
Successful students in both classes
= 20 × 80 + 30 × 60 = 16 + 18 = 34 100 100
∴ Required percentage= 34 × 100 = 68% 50
Or
Required percentage= 20 × 80 + 30 × 60 50 = 1600 + 1800 + 3400 = 68% 50 50
Aliter : Using Rule 25,
Let us take B = 20, G = 30, b = 80%, g = 60%
∴ Required percentage= Bb+ Gg B + G = 20 × 80 + 30 × 60 % 20 + 30 = 3400 = 68% 50
- In an examination 75% candidates passed in English and 60% passed in Mathematics. 25% failed in both and 240 passed the examination. Find the total number of candidates.
-
View Hint View Answer Discuss in Forum
Failures in English = 100 – 75 = 25
Failures in Maths = 100–60 = 40
Failures in both subjects = 25
Failures in English only= 25 – 25 = 0
Failures n Maths only = 40 – 25 = 15
Failures in one or both subjects = 25 + 15 = 40
Percentage of successful = 100 – 40 = 60
Let total students be x∴ x × 60 = 240 100 ⇒ x = 240 × 100 = 400 60 Correct Option: D
Failures in English = 100 – 75 = 25
Failures in Maths = 100–60 = 40
Failures in both subjects = 25
Failures in English only= 25 – 25 = 0
Failures n Maths only = 40 – 25 = 15
Failures in one or both subjects = 25 + 15 = 40
Percentage of successful = 100 – 40 = 60
Let total students be x∴ x × 60 = 240 100 ⇒ x = 240 × 100 = 400 60
