Average
- The average of marks obtained by 100 candidates in a certain examination is 30. If the average marks of passed candidates is 35 and that of the failed candidates is 10, what is the number of candidates who passed the examination?
-
View Hint View Answer Discuss in Forum
Number of successful students in the exam = p
∴ Number of unsuccessful students = 100 – p
According to the question,∴ 30 = 35p + 10(100 - p) 100
⇒ 3000 = 35p + 1000 – 10p
⇒ 3000 = 25p + 1000
⇒ 25p = 3000 – 1000 = 2000
Correct Option: C
According to the question,
∴ 30 = 35p + 10(100 - p) 100
⇒ 3000 = 35p + 1000 – 10p
⇒ 3000 = 25p + 1000
⇒ 25p = 3000 – 1000 = 2000⇒ p = 2000 = 80 25
- The average marks obtained by a class of 60 students is 65. The average marks of half of the students is found to be 85. The average marks of the remaining students is
-
View Hint View Answer Discuss in Forum
Let average marks of remaining 30 students be p.
∴ 65 = 30 × 85 + 30 × p 60
⇒ 65 × 60 = 2550 + 30p
⇒ 3900 = 2550 + 30p
⇒ 30p = 3900 – 2550 = 1350
Correct Option: B
Let average marks of remaining 30 students be p.
∴ 65 = 30 × 85 + 30 × p 60
⇒ 65 × 60 = 2550 + 30p
⇒ 3900 = 2550 + 30p
⇒ 30p = 3900 – 2550 = 1350⇒ p = 1350 = 45 30
- The average marks of 50 students in a class is 72. The average marks of boys and girls in that subject are 70 and 75 respectively. The number of boys in the class is
-
View Hint View Answer Discuss in Forum
Let Number of students in the class = n
∴ Number of girls = 50 – n
According to the question,
n × 70 + (50 – n) × 75 = 50 × 72
⇒ 70n + 3750 – 75n = 3600
⇒ 3750 – 5n = 3600
⇒ 5n = 3750 – 3600 = 150Correct Option: D
Let Number of students in the class = n
∴ Number of girls = 50 – n
According to the question,
n × 70 + (50 – n) × 75 = 50 × 72
⇒ 70n + 3750 – 75n = 3600
⇒ 3750 – 5n = 3600
⇒ 5n = 3750 – 3600 = 150⇒ n = 150 = 30 5
- The mean high temperature of the first four days of a week is 25°C whereas the mean of the last four days is 25.5°C. If the mean temperature of the whole week is 25.2°C then the temperature on the 4th day is
-
View Hint View Answer Discuss in Forum
Temperature on 4th day = (4 × 25 + 4 × 25.5 – 25.2 × 7)°C
Temperature on 4th day = (100 + 102– 176.4)°CCorrect Option: D
Temperature on 4th day = (4 × 25 + 4 × 25.5 – 25.2 × 7)°C
Temperature on 4th day = (100 + 102– 176.4)°C
Temperature on 4th day = 25.6°C
- The average weight of 8 persons increases by 2.5 kg when a new person comes in place of one of them weighing 65 kg. The weight of the new person is
-
View Hint View Answer Discuss in Forum
Weight of new person = (65 + 8 × 2.5) kg
Weight of new person = (65 + 20) kg = 85 kg
Aliter : Using Rule 23,
Here, x = 2.5, n = 8
Weight of new person = [ weight of replaced boy + x × n ]Correct Option: B
Weight of new person = (65 + 8 × 2.5) kg
Weight of new person = (65 + 20) kg = 85 kg
Aliter : Using Rule 23,
Here, x = 2.5, n = 8
Weight of new person = [ weight of replaced boy + x × n ]
Hence , Weight of new person = [ 65 + 2.5 × 8 ] = (65 + 20) kg = 85 kg
