Average - Aptitude MCQ Questions and Solutions with Explanations

$$\eqalign{ & \frac{{\left[ {\left( {10 \times 50} \right) + \left( {50 \times 10} \right) + \left( {20 \times 25} \right) + \left( {25 \times 20} \right)} \right]}}{4} \cr & = 500\,{\text{paise}} \cr} $$

$$\eqalign{ & A + B + C = 12000 \times 3 \cr & B + C + D = 15000 \times 3 \cr & \to D - A = 3000 \times 3 = 9000 \cr & {\text{Also}},\,D = 2A \cr & {\text{Then}},\,D = 18000\,{\text{and}}\,A = 9000 \cr & {\text{Therefore}}, \cr & {\text{Average}}\,{\text{salary}}\,{\text{of}}\,B\,{\text{and}}\,C, \cr & = \frac{{ {45000 - 18000} }}{2} \cr & = 13500 \cr} $$

Average Speed
$$\eqalign{ & = \frac{{2 \times 60 \times 30}}{{60 + 30}} \cr & = \frac{{3600}}{{90}} \cr & = 40\,{\text{kmph}} \cr} $$

Average of 20 students = 12 years
Total age of 20 students
= 20 × 12
= 240 years
When teacher included average become 13 years
Now, total age 20 students and teacher
= 13 × 21 = 273 years
∴ Age of teacher
= 273 - 240
= 33 years

The total wages earned during the 15 days that the worker worked ,
= 15 × 90 = Rs. 1350
The total wages earned during the first 7 days = 7 × 87 = Rs. 609
The total wages earned during the last 7 days = 7 × 92 = Rs. 644

Total wages earned during the 15 days,
= wages during first 7 days + wage on 8^th day + wages during the last 7 days.

1350 = 609 + wage on 8^th day + 644
wage on 8^th day = 1350 - 609 - 644 = Rs. 97

Let X be the number of employees.
We are given that 40% of the employees are workers.
Now, 40% of X is $$\frac{{40}}{{100}}$$ × X = 0.4X
Hence, the number of workers is $$\frac{{2{\text{X}}}}{5}$$
All the remaining employees are executives,
so the number of executives equals,
(The number of Employees) $$ - $$ (The number of Workers)
= X $$ - $$ $$\frac{{2{\text{X}}}}{5}$$
= $$\frac{{3{\text{X}}}}{5}$$
The annual income of each worker is Rs. 390.
Hence, the total annual income of all workers together is
= $$\frac{{2{\text{X}}}}{5}$$ × 390 = 156X
Also, the annual income of each executive is Rs.420.
Hence, the total income {of all the executives together is,
= $$\frac{{3{\text{X}}}}{5}$$ × 420 = 252X
Hence, the total income of the employees is,
= 156X + 252X = 408X
The average income of all the employees together = 408

Total cost of 10 books = Rs. 120
Total cost of 8 books = Rs. 94
⇒ The cost of 2 books = Rs. 26
Let the price of each book be x and y.
⇒ x + y = 26 - - - - - - (1)
$$\left( {\frac{{160}}{{100}}} \right)x + y = 26$$
On Solving for y, we get
y = 10
Now, Substituting y = 10 in (1) we get,
x + 10 = 26
x = 16
So the price of each book is Rs. 16 and Rs. 10 respectively.

$$\eqalign{ & {\text{Let}}\,{\text{the}}\,{\text{three}}\,{\text{numbers}}\,{\text{be}}\,x,\,y,\,{\text{and}}\,z.\, \cr & {\text{We}}\,{\text{are}}\,{\text{given}}\,{\text{that}}\, \cr & \frac{{ {x + y} }}{2} = 2 \cr & \frac{{ {y + z} }}{2} = 3 \cr & \frac{{ {x + z} }}{2} = 4 \cr & {\text{Adding}}\,{\text{three}}\,{\text{equations}}, \cr & \frac{{ {x + y} }}{2} + \frac{{ {y + z} }}{2} + \frac{{ {x + z} }}{2} = 2 + 3 + 4 \cr & x + y + z = 9 \cr & {\text{The}}\,{\text{average}}\,{\text{of}}\,{\text{the}}\,{\text{three}}\,{\text{numbers}}\,{\text{is}}, \cr & \frac{{ {x + y + z} }}{3} = \frac{9}{3} = 3 \cr} $$

$$\eqalign{ & {\text{Let}}\,{\text{three}}\,{\text{numbers}}\,{\text{be}}\,x,\,y,\,z. \cr & {\text{Given}}, \cr & x = 2y \cr & \Rightarrow x = 4z \cr & \Rightarrow y = 2z \cr & \Rightarrow z = z \cr & {\text{The}}\,{\text{average}}\,{\text{of}}\,{\text{reciprocal}}\,{\text{numbers}}\,{\text{is}}\,\frac{7}{{72}} \cr & \frac{{ { {\frac{1}{x}} + {\frac{1}{y}} + {\frac{1}{z}} } }}{3} = \frac{7}{{72}} \cr & \Rightarrow \frac{{ {yz + xz + xy} }}{{3xyz}} = \frac{7}{{72}} \cr & \Rightarrow \frac{{2z \times z + 4z \times z + 4z \times 2z}}{{3\left( {4z \times 2z \times z} \right)}} = \frac{7}{{72}} \cr & \Rightarrow \frac{{2{z^2} + 4{z^2} + 8{z^2}}}{{3 \times 8{z^3}}} = \frac{7}{{72}} \cr & \Rightarrow \frac{{14{z^2}}}{{24{z^3}}} = \frac{7}{{72}} \cr & \Rightarrow 504 = 84z \cr & z = 6 \cr & {\text{So}},\,x = 4z = 4 \times 6 = 24, \cr & \Rightarrow y = 2z = 2 \times 6 = 12 \cr & {\text{Thus}}\,{\text{the}}\,{\text{numbers}}\,{\text{are}}\,24,\,12,\,6 \cr} $$

The total salary amount = 15 × 600 = 9000
The salary of the exiting manager = 720
Therefore, the salary of 12 workers and the remaining 2 managers,
= 9000 − 720 = 8280
When a new manager joins, the new average salary drops to Rs. 580 for the total team of 15 of them
The total salary for the 15 people i.e., 12 workers, 2 old managers and 1 new manager =580 × 15 = 8700
Therefore, the salary of the new manager is,
9000 - 8700 = 300 less than that of the old manager who left the company, which is equal to 720 - 300 = 420

Alternatively,
The average salary dropped by Rs. 20 for 15 of them.
Therefore, the overall salary has dropped by 15 × 20=300
Therefore, the new manager's salary should be Rs. 300 less than that of the old manager,
= 720 - 300
= 420