Average - Aptitude MCQ Questions and Solutions with Explanations

According to the question,
Average age of a family of 10 members is = 20 years
Sum of the age of 10 members = 20 × 10 = 200 years
If the age of youngest member is = 10 years
Sum of the age of 9 members at the time of birth of youngest member
= 200 - 10 × 10
= 200 - 100
= 100 years
∴ Average age of 9 members is
$$\eqalign{ & = \frac{{100}}{9} \cr & = 11\frac{1}{9}{\text{ years}} \cr} $$

The sum of last three numbers = 47 × 3 + 10 = 151
\[\begin{array}{*{20}{c}} {\,{{11}^{{\text{th}}}}}&{{{12}^{{\text{th}}}}}&{{{13}^{{\text{th}}}}} \\ {2x}&x&{x + 3} \end{array}\]
Sum of 11^th, 12^th and 13^th ;
2x + x + x + 3 = 151
4x + 3 = 151
x = 17
Average of 11^th of 13^th
$$\eqalign{ & = \frac{{2x + x + 3}}{2} \cr & = \frac{{3\left( {x + 1} \right)}}{2} \cr & = 3 \times \frac{{38}}{2} \cr & = 57 \cr} $$

Average of 7 consecutive odd numbers = A   (Given)
Then 7 number consecutive odd numbers = - - - A - - -
According to the question,
If next 4 and previous 3 odd numbers are also included the numbers of terms = 7 + 3 + 4 = 14, and effected sum of numbers = 2 × 7 = 14
∴ Increment of average $$ = \frac{{14}}{{14}} = 1$$
∴ Required average = A + 1

Sum of 16 numbers = 16 × 48 = 768
Sum of first 6 numbers = 6 × 45 = 270
Sum of last 7 numbers = 7 × 53 = 371
\[\begin{array}{*{20}{c}} {{7^{{\text{th}}}}}&{{8^{{\text{th}}}}}&{\,\,\,{9^{{\text{th}}}}} \\ {\left( {x + 3} \right)}&{\left( {x + 7} \right)}&{\left( x \right)} \end{array}\]
$$\eqalign{ & \Rightarrow 3x = 127 - 10 \cr & \Rightarrow x = 39 \cr & \therefore {\text{Average of}}\,{{\text{9}}^{{\text{th}}}}\,{\text{and}}\,{{\text{7}}^{{\text{th}}}}\,{\text{number}} \cr & = \frac{{x + \left( {x + 3} \right)}}{2} \cr & = \frac{{2x + 3}}{2} \cr & = x + 10.5 \cr & = 39 + 1.5 \cr & = 40.5 \cr} $$

$$\eqalign{ & 14,\,21\,......\,70 \cr & \mathop {8 - - - - - - - 74}\limits_{{\text{Divisible by 7}}} \cr & {\text{Number of items}} = \frac{{{\text{Lat term}} - {\text{First term}}}}{{{\text{Common Difference}}}} + 1 \cr & = \frac{{70 - 14}}{7} + 1 \cr & = 9 \cr & {\text{Average of all number divisible by 7}} \cr & \Rightarrow \frac{n}{{2 \times n}}\left[ {a + l} \right] \cr & \Rightarrow \frac{{84}}{2} \cr & \Rightarrow 2 \cr} $$

$$\eqalign{ & \frac{{a + b}}{2} + c = 164 \cr & \frac{{b + c}}{2} + a = 158 \cr & \frac{{c + a}}{2} + b = 132 \cr & \overline {\frac{{2\left( {a + b + c} \right)}}{2} + a + b + c = 454} \cr & a + b + c = 227 \cr & {\text{Average}} = \frac{{a + b + c}}{3} = \frac{{227}}{3} = 75\frac{2}{3} \cr} $$

According to the question,
Annual income = 1,000 × 12 = Rs. 12,000
Annual expenditure = 1,000 × 9 = Rs. 9,000
Savings = Rs. 12,000 - Rs. 9,000 = Rs. 3,000

$$\eqalign{ & {\text{Given,}} \cr & \therefore {\text{Total cost of the 7 machines}} \cr & = 95000 \times 2 + 75000 \times 2 + 43000 \times 3 \cr & = 190000 + 150000 + 129000 \cr & = {\text{Rs}}{\text{. }}469000 \cr & \because {\text{Average}} = \frac{{{\text{Total cost}}}}{{{\text{Total number of machines}}}} \cr & = \frac{{469000}}{7} \cr & = {\text{Rs}}{\text{. }}67000 \cr} $$

Total age of 7 students = 7 x 28 = 196 years
Total age of first 3 students = 3 x 30 = 90 years
5^th student age = x years
4^th student age = (x + 4) years
Age of 6^th and 7^th student = 30 + 5 = 35 years
Total age of 7 students = 196
⇒ 90 + (x + 4) + (x) + 35 + 35 = 196
⇒ 2x = 196 - 164
⇒ 2x = 32
∴ x = 16 years
Average of 4^th and 5^th student
$$\eqalign{ & = \frac{{\left( {x + 4} \right) + x}}{2} \cr & = \frac{{2 \times 16 + 4}}{2} \cr & = 18{\text{ years}} \cr} $$

Total earning in January = 925 × 31 = Rs. 28675
Earning of first 20 days = 881 × 20 = Rs. 17620
Earning of last 20 days = 915 × 20 = Rs. 18300
Earning of 12^th January to 20^th January = (17620 + 18300) - 28675
= 35920 - 28675
= Rs. 7245
∴ Average of earning of 12^th January to 20^th January
$$\eqalign{ & = \frac{{7245}}{9} \cr & = {\text{Rs}}{\text{. 805}} \cr} $$