## Average Questions and Answers Part-11

1. Which one of the following numbers can be removed from the set S = {0, 2, 4, 5, 9} without changing the average of set S?
a) 0
b) 2
c) 4
d) 5

Explanation: The average of the elements in the original set S is:
\eqalign{ & \frac{{0 + 2 + 4 + 5 + 9}}{5} \cr & = \frac{{20}}{5} \cr & = 4 \cr}
If we remove an element that equals the average, then the average of the new set will remain unchanged. The new set after removing 4 is {0, 2, 5, 9}.
Average of the elements,
\eqalign{ & \frac{{0 + 2 + 5 + 9}}{4} \cr & = \frac{{16}}{4} \cr & = 4 \cr}

2. Average cost of 5 apples and 4 mangoes is Rs. 36. The average cost of 7 apples and 8 mangoes is Rs. 48. Find the total cost of 24 apples and 24 mangoes
a) 1044
b) 2088
c) 720
d) 3240

Explanation: Average cost of 5 apples and 4 mangoes = Rs. 36
Total cost = 36 × 9 = 324
Average cost of 7 apples and 8 mangoes = 48
Total cost = 48 × 15 = 720
Total cost of 12 apples and 12 mangoes = 324 + 720 = 1044
Cost of 24 apples and 24 mangoes = 1044 × 2 = 2088

3. The average weight of three boys A, B and C is $$\frac{{163}}{3}$$ kg, while the average weight of three boys B, D and E is 53 kg. What is the average weight of A, B, C, D and E?
a) 52.4 kg
b) 53.2 kg
c) 53.8 kg

Explanation: In this question, sum of numbers is provided, net required sum (i.e. A + B+ C+ D + E) cannot be calculated by the given data.

4. Average of ten positive numbers is x. If each number is increased by 10%, then x :
a) remains unchanged
b) may decrease
c) may increase
d) is increased by 10%

Explanation: Let 10 numbers be x1, x2, x3, . . . . . . . x10
Average of these 10 numbers is 10
$$\frac{{ {x1 + x2 + x3 + .... + x10} }}{{10}} = x$$
Now if each number is increased by 10%,
then new average, say y.
$$y = \frac{{ {1.1x1 + 1.1x2 + 1.1x3 + .... + 1.1x10} }}{{10}}$$
$${\kern 1pt} y = 1.1 \times {\frac{{ {x1 + x2 + x3 + .... + x10} }}{{10}}}$$
\eqalign{ & y = 1.1x \cr & y\,{\text{is }}10\% \,{\text{increased}} \cr}

5. The average price of 10 books is Rs.12 while the average price of 8 of these books is Rs. 11.75. Of the remaining two books, if the price of one book is 60% more than the price of the other, what is the price of each of these two books?
a) Rs. 5, Rs.7.50
b) Rs. 8, Rs. 12
c) Rs. 10, Rs. 16
d) Rs. 12, Rs. 14

Explanation: 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)
Given that the price of 1 book is 60% more than the other price
\eqalign{ & \left( {\frac{{160}}{{100}}} \right)y + y = 26 \cr & y\left( {\frac{{160}}{{100}} + 1} \right) = 26 \cr & y\left( {\frac{{160 + 100}}{{100}}} \right) = 26 \cr & y = \frac{{\left( {26 \times 100} \right)}}{{260}} \cr & y = 10 \cr & {\text{Substituting}}\,\,y = 10\,\,{\text{in }}{\kern 1pt} \left(1 \right), \cr & x + 10 = 26 \cr & x = 16 \cr}

6. Distance between two stations A and B is 778km. A train covers the journey from A to B at 84km per hour and returns back to A with a uniform speed of 56km per hour. Find the average speed of train during the whole journey.
a) 60 km/hr
b) 30.5 km/hr
c) 57 km/hr
d) 67.2 km/hr

Explanation:
\eqalign{ & {\text{Average speed}} = {\frac{{2xy}}{{ {x + y} }}} {\kern 1pt} {\kern 1pt} {\text{km/hr}} \cr & = {\frac{{ {2 \times 84 \times 56} }}{{ {84 + 56} }}} {\kern 1pt} {\kern 1pt} {\text{km/hr}} \cr & = {\frac{{ {2 \times 84 \times 56} }}{{140}}} {\kern 1pt} {\kern 1pt} {\text{km/hr}} \cr & = 67.2{\kern 1pt} {\kern 1pt} {\text{km/hr}} \cr}

7. The average of 50 numbers is 30. If two numbers, 35 and 40 are discarded, then the average of the remaining numbers is nearly:
a) 28.32
b) 29.68
c) 28.78
d) 29.27

Explanation: Total sum of 48 numbers =
(50 × 30) - (35 + 40)
1500 - 75 = 1425
Average = $$\frac{{1425}}{{48}}$$ = 29.68

8. The average score of a cricketer for ten matches is 38.9 runs. If the average for the first six matches is 42, then find the average for the last four matches
a) 33.25
b) 33.5
c) 34.25
d) 35

Explanation: Total sum of last 4 matches,
= (10 × 38.9) - (6 × 42)
= 389 - 252 = 137
Average = $$\frac{{137}}{4}$$ = 34.25

9. Nine persons went to a hotel for taking their meals. Eight of them spent Rs.12 each on their meals and the ninth spent Rs.8 more than the average expenditure of all the nine. What was the total money spent by them.
a) Rs. 115
b) Rs. 116
c) Rs. 117
d) Rs. 118

Explanation: Let the average expenditure of all the nine be Rs. X
12 × 8 + (X + 8) = 9X
X = 13
Total money spent = 9X
= Rs. (9 × 13)
= Rs. 117

10. The average of runs of a cricket player of 10 innings was 32. How many runes must be made in his next innings so as to increase his average of runs by 4?
a) 72
b) 74
c) 70
d) 76