1. The mean weight of 100 students in a class is 46 kg. The mean weight of boys is 50 and of girls is 40 kg. Therefore, the number of boys is:
a) 50
b) 60
c) 70
d) 65
Explanation: Let number of boys are x and then number of girls
= (100 - x)
50x + (100 - x) × 40 = 46 × 100
x = 60
Number of boys = 60
2. The average income of A, B and C is Rs. 12,000 per month and average income of B, C and D is Rs. 15,000 per month. If the average salary of D be twice that of A, then the average salary of B and C is in Rs. :
a) 13,500
b) 9,000
c) 8,000
d) 18,000
Explanation:
$$\eqalign{ & A + B + C = 12000 \times 3 \cr & B + C + D = 15000 \times 3 \cr & \to D - A = 3000 \times 3 = 9000 \cr & \,D = 2A \cr & \,D = 18000\,{\text{and}}\,A = 9000 \cr & {\text{Therefore}}, \cr & {\text{Average}}\,{\text{salary}}\,{\text{of}}\,B\,{\text{and}}\,C, \cr & = \frac{{ {45000 - 18000} }}{2} \cr & = 13500 \cr} $$
3. The average marks of four subjects is 120. If 33 was misread as 13 during the calculation, what will be the correct average?
a) 122
b) 120
c) 125
d) 121
Explanation:
$$\eqalign{ & {\text{Correct average}} \cr & = 120 + \left( {\frac{{33 - 13}}{4}} \right) \cr & = 120 + 5 \cr & = 125 \cr} $$
Average given is 120.
Difference of 33 and 13 is 20.
That means 20 must be added to total.
Then average of is and so must be added to average, i.e.
Correct average = 120 + 5 = 125
4. Find the average increase rate, if increase in the population in the first year is 30% and that in the second year is 40%.
a) 41%
b) 56%
c) 40%
d) 38%
Explanation: Let 100 be the original population.
1st year's population increased = 30%
So, Population after first year
= (100 + 30% of 100)
= 130
Population in second year increases by 40%,
Then Population
= (130 + 40% of 130)
= 182
The final population become 182 which was originally at 100.
It means there is 82% increment in the population in 2 years
So, Average increment = $$\frac{{82}}{2}$$ = 41%
5. The average weight of 47 balls is 4 g. if the weight of the bag (in which the balls are kept) be included; the calculated average weight per ball increases by 0.3 g. What is the weight of the bag?
a) 14.8 g
b) 14.4 g
c) 15 g
d) 14.1 g
Explanation: Total increased weight
= 0.3 × 47
= 14.1 g
6. The average of 20 students is 12 years, if the teacher's age is included, average increases by one. The age of the teacher is:
a) 28 years
b) 30 years
c) 33 years
d) 35 years
Explanation: 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
7. The average monthly salary of 660 workers in a factory is Rs. 380. The average monthly salary of officers is Rs. 2100 and the average monthly salary of the other workers is Rs. 340. Find the number of other workers.
a) 645
b) 650
c) 640
d) 642
Explanation:
$$\eqalign{ & {\text{Total}}\,{\text{salary}}\,{\text{of}}\,660\,{\text{workers}} \cr & = 660 \times 380 \cr & = Rs.\,250800 \cr & {\text{If}}\,{\text{other}}\,{\text{workers}}\,{\text{be}}\,x;\,{\text{then}}, \cr & = \left[ {\left( {660 - x} \right) \times 2100} \right] + 340x \cr & = 250800 \cr & \,1386000 - 2100x + 340x = 250800 \cr & 1760x = 1135200 \cr & \,x = \frac{{1135200}}{{1760}} = 645 \cr & {\text{Number}}\,{\text{of}}\,{\text{other}}\,{\text{workers}} = 645 \cr} $$
8. 19 people went to a hotel for combine dinner party 13 of them spent Rs. 79 each on their dinner and rest spent 4 more than the average expenditure of all the 19. What was the total money spent by them.
a) 1628.4
b) 1534
c) 1496
d) None of these
Explanation: Let average expenditure of 19 people be x
19x = 13 × 79 + 6 × (x + 4)
19x = 13 × 79 + 6x + 24
x = 80.84
So, total money spent
= 80.84 × 19
= Rs. 1536.07
9. Students of three different classes appeared in common examination. Pass average of 10 students of first class was 70%, pass average of 15 students of second class was 60% and pass average of 25 students of third class was 80% then what will be the pass average of all students of three classes?
a) 69%
b) 72%
c) 74%
d) 75%
Explanation:
$$\eqalign{ & {\text{Sum}}\,{\text{of}}\,{\text{pass}}\,{\text{student}}\,{\text{}}\,{\text{first,}}\,{\text{second}}\,{\text{and}}\,{\text{third}}\,{\text{class}}, \cr & = \left( {70\% \,{\text{of}}\,10} \right) + \left( {60\% \,{\text{of}}\,15} \right) + \left( {80\% \,{\text{of}}\,25} \right) \cr & = 7 + 9 + 20 = 36 \cr & {\text{Total}}\,{\text{students}}\,{\text{appeared}}, \cr & = 10 + 15 + 25 = 50 \cr & {\text{Pass}}\,{\text{average}}, \cr & = 36 \times \frac{{100}}{{50}} = 72\% \cr} $$
10. A passenger travels from Delhi to Merut at a speed of 30 kmph and return with a speed of 60 kmph. What is the average speed?
a) 45
b) 48
c) 40
d) 50
Explanation: Average Speed
$$\eqalign{ & = \frac{{2 \times 60 \times 30}}{{60 + 30}} \cr & = \frac{{3600}}{{90}} \cr & = 40\,{\text{kmph}} \cr} $$