MCQ on Average | Page 10 of 10 | for Competitive exams with answers

mcq on averages for ssc gd

Solve the following MCQ on average:

The average monthly income of P and Q is Rs.5, 050. The average monthly income of Q and R is Rs. 6, 250 and the average monthly income of P and R is Rs. 5,200. The monthly income of P is

(1) 3, 500

(2) 4, 000

(3) 4, 050

(4) 5, 000

Answer: (2)
Total monthly income of P and Q = 2 × 5050 = 10100
Total monthly income of Q and R = 2 × 6250 = 12500
Total monthly income of P and R = 2 × 5200 = 10400
On adding all three,
Total monthly income of 2(P + Q + R)
= (10100 + 12500 + 10400)
= 33000
Therefore, Total monthly income of (P + Q + R)
\(\displaystyle =\frac{{33000}}{2}=16500\)
Hence, P’s monthly income
= (16500 – 12500)
= 4000

Of the three numbers, first is twice the second and second is twice the third. The average of three numbers is 21. The smallest of the three numbers is

(1) 9

(2) 6

(3) 12

(4) 18

Answer: (1)
Let the third number be x.
Therefore, the second number = 2x
and the third number = 2 × 2x = 4x
According to the question,
\(\displaystyle \begin{array}{l}=\frac{{4x+2x+x}}{3}=21\\\Rightarrow 7x=21\times 3\\\Rightarrow x=\frac{{21\times 3}}{7}=9\end{array}\)

Out of three numbers, the first is twice the second and is half of the third. If the average of the three numbers is 56, then difference of first and third number is

(1) 12

(2) 20

(3) 24

(4) 48

Answer: (4)
Let the numbers be 2x, x and 4x respectively
Average \(\displaystyle \begin{array}{l}=\frac{{2x+x+4x}}{3}=56\\\Rightarrow 7x=56\times 3\\\Rightarrow x=\frac{{56\times 3}}{7}=24\end{array}\)
Therefore, frst number = 2x = 2 × 24 = 48
Third number = 4x = 4 × 24 = 96
Required difference = 96 – 48 = 48

The average of marks of 14 student was calculated as 71. But it was later found that the marks of one student had been wrongly entered as 42 instead of 56 and of another as 74 instead of 32. The correct average is :

(1) 67

(2) 68

(3) 69

(4) 71

Answer: (3)
According to question,
Total marks = 71 × 14 = 994
Correct total marks
= 994 + (56 – 42) + (32 – 74)
= 994 + 14 – 42 = 966
Required average = \(\displaystyle \frac{{966}}{{14}}=69\)
Other Method:
Using Rule, If the average of n numbers is m later on it was found that two numbers a and b misread as p and q.
The correct average = \(\displaystyle m+\frac{{(a+b-p-q)}}{n}\)
Here n = 14, m = 71
a = 56, b = 42
p = 32, q = 74
Correct Average \(\displaystyle \begin{array}{l}=71+\frac{{(56+32-42-74)}}{{14}}\\=71-\frac{{28}}{{14}}=69\end{array}\)

The average weight of three men A, B and C is 84 kg. D joins them and the average weight of the four becomes 80 kg. If E whose weight is 3 kg more than that of D, replaces A, the average weight of B, C, D and E becomes 79 kg. The weight of A is

(1) 65 kg.

(2) 70 kg.

(3) 75 kg.

(4) 80 kg.

Answer: (3)
Total weight of A, B and C = 84 × 3 = 252 kg.
Again, A + B + C + D = 80 × 4 = 320 kg.
Therefore, D = (320 – 252) = 68 kg.
E = 68 + 3 = 71 kg.
B + C + D + E = 79 × 4 = 316 kg.
Now,
(A + B + C + D) – (B + C + D +E) = (320 – 316) kg.
A – E = 4 kg.
or A = 4 + E = 4 + 71 = 75 kg.

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