1. There were 35 students in a hostel. Due to the admission of 7 new students the expenses of the mess were increased by Rs.42 per day while the average expenditure per head diminished by Re 1. What was the original expenditure of the mess?
a) Rs. 450
b) Rs. 320
c) Rs. 550
d) Rs. 420
Explanation: Let the original average expenditure be Rs. x
42(x - 1) - 35x = 42
7x = 84
x = 12
Original expenditure,
= Rs. (35 × 12)
= Rs. 420
2. 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 x
12 × 8 + (x + 8) = 9x
x = 13
Total money spent = 9x
= Rs. (9 × 13)
= Rs. 117
3. David obtained 76, 65, 82, 67 and 85 marks (out of 100) in English, mathematics, physics, chemistry and biology. What are his average marks?
a) 65
b) 69
c) 75
d) None of these
Explanation:
$$\eqalign{ & {\text{Average}} \cr & = \frac{{ {76 + 65 + 82 + 67 + 85} }}{5} \cr & = \frac{{375}}{5} \cr & = 75 \cr} $$
4. 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
Explanation: Average after 11 innings = 36
Required number of runs = ( 36 × 11) - (32 × 10)
= 396 - 320
= 76
5. There are two sections A and B of a class, consisting of 36 and 44 students respectively. If the average weight of section A is 40kg and that of section B is 35kg, find the average weight of the whole class
a) 30 kg.
b) 35 kg.
c) 42.5 kg
d) 37.25 kg.
Explanation: Total weight of (36 + 44) Students,
= (36 × 40 + 44 × 35) kg
= 2980 kg
Average weight of the whole class,
= $$ {\frac{{2980}}{{80}}} $$ kg.
Average weight = 37.25 kg.
6. The average age of three boys is 15 years. If their ages are in ratio 3 : 5 : 7, the age of the youngest boy is
a) 21 years
b) 18 years
c) 15 years
d) 9 years
Explanation: Sum of ages of three boys = 45 years
3x + 5x + 7x = 45
15x = 45
x = 3
Age of youngest boy = 3x
= 3 × 3 = 9 years
7. The average of a group of men is increased by 5 years when a person aged of 18 years is replaced by a new person of aged 38 years. How many men are there in the group?
a) 3
b) 4
c) 5
d) 6
Explanation: Let N be the no. of persons in the group.
Required number of person is given by;
Member in group × aged increased = difference of replacement
N × 5 = 38 - 18
5N = 20
N = 4
8. In a boat there are 8 men whose average weight is increased by 1 kg when 1 man of 60 kg is replaced by a new man. What is weight of new comer?
a) 70 kg
b) 66 kg
c) 68 kg
d) 69 kg
Explanation: Member in group × age increased = difference of replacement
8 × 1 = new comer - man going out
new comer = 8 + 60
new comer = 68 kg.
9. The average of 25 results is 18. The average of first 12 of those is 14 and the average of last 12 is 17. What is the 13th result?
a) 74
b) 75
c) 69
d) 78
Explanation: Sum of 1st 12 results = 12 × 14
Sum of last 12 results = 12 × 17
13th result = x (let)
12 × 14 + 12 × 17 + x = 25 × 18
x = 78
10. A train covers the first 16 km at a speed of 20 km per hour another 20 km at 40 km per hour and the last 10 km at 15 km per hour. Find the average speed for the entire journey.
a) 24 km
b) 26 km
c) 21 km
d) \[23\frac{{23}}{{59}}\] km
Explanation:
$$\eqalign{ & {\text{Average}}\,{\text{speed}} \cr & = \frac{{{\text{total}}\,{\text{distance}}\,{\text{covered}}}}{{{\text{total}}\,{\text{time}}}} \cr & {\text{Total}}\,{\text{Distance}} = {16 + 20 + 10} \cr & = 46\,{\text{km}} \cr & {\text{Time}}\,{\text{taken}} = {\frac{{16}}{{20}}} + {\frac{{20}}{{40}}} + {\frac{{10}}{{15}}} \cr & = {\frac{{4}}{{5}}} + {\frac{{1}}{{2}}} + {\frac{{2}}{{3}}} \cr & = {\frac{{24 + 15 + 20}}{{30}}} \cr & = \frac{{59}}{{30}} \cr & {\text{Average}}\,{\text{speed}} \cr & = \frac{{46 \times 30}}{{59}} \cr & = 23\frac{{23}}{{59}}\,{\text{km/hr}} \cr} $$