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
(a) 84 kg
(b) 85 kg
(c) 76 kg
(d) 76.5 kg
(e) 82 kg
Answer: (b)
Weight of new person
= (65 + 8 × 2.5) kg
= (65 + 20) kg
= 85 kg
Three Science classes A, B and C take a Life Science test. The average score of class A is 83. The average score of class B is 76. The average score of class C is 85. The average score of class A and B is 79 and average score of class B and C is 81. Then the average score of classes A, B and C is
(a) 81.5
(b) 81
(c) 80.5
(d) 80
(e) 82
Answer: (a)
Let,
Students in class A = x
Students in class B = y
Students in class C = z
For classes A and B,
\(\displaystyle \frac{{83x+76y}}{{x+y}}=79\)
\(\displaystyle \Rightarrow \)83x + 76y = 79x + 79y
83x – 79x = 79y – 76y
\(\displaystyle \Rightarrow \)4x = 3y
For classes B and C
\(\displaystyle \frac{{76y+85z}}{{y+z}}=81\)
76y + 85z = 81y + 81z
\(\displaystyle \Rightarrow \)5y = 4z
Therefore,
20x = 15y = 12z
\(\displaystyle \frac{{20x}}{{60}}=\frac{{15y}}{{60}}=\frac{{12z}}{{60}}\)
\(\displaystyle \frac{x}{3}=\frac{y}{4}=\frac{z}{5}\)
Required average = \(\displaystyle \frac{{83\times 3+76\times 4+85\times 5}}{{3+4+5}}\)
\(\displaystyle \frac{{249+304+425}}{{12}}=\frac{{978}}{{12}}=81.5\)
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
(a) 20
(b) 35
(c) 25
(d) 30
(e) 40
Answer: (d)
Number of students in the class = x (let)
Number of girls = 50 – x
According to the question,
x × 70 + (50 – x) × 75
= 50 × 72
\(\displaystyle \Rightarrow \) 70x + 3750 – 75x = 3600
\(\displaystyle \Rightarrow \) 3750 – 5x = 3600
\(\displaystyle \Rightarrow \) 5x = 3750 – 3600 = 150
\(\displaystyle x=\frac{{150}}{5}=30\)
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?
(a) 60
(b) 70
(c) 80
(d) 90
(e) 50
Answer: (c)
Number of successful students in the exam = x
Number of unsuccessful students = 100 – x
According to the question,
\(\displaystyle 30=\frac{{35x+10(100-x)}}{{100}}\)
\(\displaystyle \Rightarrow \) 3000 = 35x + 1000 – 10x
\(\displaystyle \Rightarrow \) 3000 = 25x + 1000
\(\displaystyle \Rightarrow \) 25x = 3000 – 1000 = 2000
\(\displaystyle x=\frac{{2000}}{{25}}=80\)
The average of 100 observations was calculated as 35. It was found later, that one of the observations was misread as 83 instead of 53. The correct average is :
