Solve the following MCQ on Average and Check your answers:
The average of the marks obtained in an examination by 8 students was 51 and by 9 other students was 68. The average marks of all 17 students was:
(1) 59
(2) 59.5
(3) 60
(4) 60.5
Solution: (3)
Sum of total number of 8 students in exam = 8 × 51 = 408
Sum of total number of 9 students in exam = 9 × 68 = 612
Required average \(\displaystyle =\frac{{408+612}}{{17}}=\frac{{1020}}{{17}}=60\)
12 kg of rice costing Rs. 30 per kg is mixed with 8 kg of rice costing Rs. 40 per kg. The average per kg price of mixed rice is
(1) 38
(2) 37
(3) 35
(4) 34
Solution: (4)
Total cost price of 20kg of mixed rice = (12 × 30 + 8 × 40) = 680
Average per kg price = 680 20 = 34
Alternate method :
Here,
\(\displaystyle \begin{array}{l}{{x}_{1}}=12,{{A}_{1}}=30\\{{x}_{2}}=8,{{A}_{2}}=40\end{array}\)
Average= \(\displaystyle \frac{{{{A}_{1}}{{x}_{1}}+{{A}_{2}}{{x}_{2}}}}{{{{x}_{1}}+{{x}_{2}}}}\)
\(\displaystyle \begin{array}{l}=\frac{{30\times 12+40\times 8}}{{12+8}}\\=\frac{{360+320}}{{20}}\\=\frac{{680}}{{20}}=34\end{array}\)
The average of 20 numbers is 15 and the average of first five is 12. The average of the rest is
(1) 16
(2) 15
(3) 14
(4)13
Solution: (1)
If the average of remaining numbers be x, then
20 × 15 = 5 × 12 + 15x
300 = 60 + 15x
15x = 300 – 60 = 240
x = 240 /15 = 16
Alternate method
Average of remaining Numbers = \(\displaystyle \frac{{mx-ny}}{{m-n}}\)
Here, m = 20, x = 15
n = 5, y = 12
Therefore,
\(\displaystyle \begin{array}{l}=\frac{{20\times 15-5\times 12}}{{20-5}}\\=\frac{{300-60}}{{15}}\\=\frac{{240}}{{15}}=16\end{array}\)
The average monthly salary of all the employees in an industry is 12,000. The average salary of male employees is 15,000 and that of female employees is 8,000. What is the ratio of male employees to female employees ?
(1) 5 : 2
(2) 3 : 4
(3) 4 : 3
(4) 2 : 5
Solution: (3)
Male employees = x
Female employees = y
Therefore,
(x + y) 12000 = x × 15000 + y × 8000
(x + y) × 12 = 15x + 8y
12x + 12y = 15x + 8y
3x = 4y
x/y =4/3
hence, x : y = 4 : 3
The mean of 9 observations is 16. One more observation is included and the new mean becomes 17. The 10th observation is
(1) 9
(2) 16
(3) 26
(4) 30
Answer: (3)
Tenth observation = Mean of Ten observations – Mean of nine observations
Tenth observation = 10 × 17 – 16 × 9 = 170 – 144 = 26
Alternate Method :
Using Rule shortcut,
The average age of a group of N students is ‘T’ years. If ‘n’ students join, the average age of the group increases by ‘t’ years, then Average age of new students
= T + \(\displaystyle \frac{N}{n}\) = 1 × t
Here, N = 9, T = 16 n = 1, t = 1 10th observation
10th observation = = T + \(\displaystyle \frac{N}{n}\) = 1 × t
= 16+ \(\displaystyle \frac{9}{1}+1\times 1\)
= 16+10 = 26
