1. My Scooty gives an average of 40 kmpl of petrol. But after recent filling at the new petrol pump, its average dropped to 38 kmpl. I investigated and found out that it was due to adulterated petrol. Petrol pimps add kerosene, which is $$\frac{2}{3}$$ cheaper than petrol, to increase their profits. Kerosene generates excessive smoke and knocking and gives an average of 18 km per 900 ml. If I paid Rs. 30 for a litre of petrol, What was the additional amount the pump-owner was making?
a) Rs. 1.75
b) Rs. 1.80
c) Rs. 2
d) Rs. 2.30
Explanation: Let x ml of kerosene be there in 1 litre mixture.
Then, quantity of petrol in 1 litre mixture = (1000 - x) ml
$$ \frac{{40}}{{1000}}\left( {1000 - x} \right)$$ $$ + \frac{{18}}{{900}}x$$ = 38
$$\eqalign{ & \frac{x}{{25}} - \frac{x}{{50}} = 2 \cr & \frac{x}{{50}} = 2 \cr & x = 100 \cr} $$
So, 1 litre mixture has 900 ml petrol and 100 ml kerosene.
Cost of 1 litre petrol = Rs. 30
Cost of 1 litre kerosene
= Rs. $$\left[ {\left( {1 - \frac{2}{3}} \right) \times 30} \right]$$
= Rs. 10
Coast of 1 litre mixture
= Rs. $$\left( {\frac{{30}}{{1000}} \times 900 + \frac{{10}}{{1000}} \times 100} \right)$$
= Rs. 28
Additional amount earned by pump-owner
= Rs. (30 - 28)
= Rs. 2
2. The body weight of seven students of a class is recorded as 54 kg, 78 kg, 43 kg, 82 kg, 67 kg, 42 kg and 75 kg. What is the average body weight of call the seven students?
a) 63 kg
b) 69 kg
c) 741 kg
d) 73 kg
Explanation: Average body weight
$$\eqalign{ & = {\frac{{54 + 78 + 43 + 82 + 67 + 42 + 75}}{7}} {\text{ kg}} \cr & = {\frac{{441}}{7}} {\text{ kg}} = 63{\text{ kg}} \cr} $$
3. There are five boxes in a cargo hold. The weight of the first box is 200 kg and the weight of the second box is 20% more than the weight of third box, whose weight is 25% more than the first box’s weight. The fourth box at 350 kg is 30% lighter than the fifth box. The difference in the average weight of the four heaviest boxes and the four lightest boxes is
a) 37.5 kg
b) 51.5 kg
c) 75 kg
d) 112.5 kg
Explanation: Weight of first box = 200 kg
Weight of third box
= 125 % of 200 kg
= 250 kg
Weight of second box
= 120% of 250 kg
= 300 kg
Weight of fourth box = 350 kg
Let the weight of fifth box be x kg
70% of x = 350 kg
$$\eqalign{ & x = \left( {\frac{{350 \times 100}}{{70}}} \right) \cr & x = 500{\text{ kg}} \cr} $$.
Average weight of four heaviest boxes
$$\eqalign{ & {\text{ = }}\left( {\frac{{500 + 350 + 300 + 250}}{4}} \right){\text{kg}} \cr & {\text{ = 350 kg}} \cr} $$
Average weight of four lightest boxes
$$\eqalign{ & = \left( {\frac{{200 + 250 + 300 + 350}}{4}} \right){\text{kg}} \cr & = 275{\text{ kg}} \cr} $$
Required difference
= (350 - 275)
= 75 kg
4. The average of 4 positive integers is 59. The highest integer is 83 and the lowest integer is 29. The difference between the remaining two integers is 28. Which of the following integers is higher of the remaining two integers ?.
a) 39
b) 48
c) 76
d) Cannot be determined
Explanation: Sum of four integers = 59 × 4 = 236
Let the required integers be x and x -28
x + (x - 28) = 236 - (83 + 29)
2x - 28 = 124
2x = 152
x = 76
Required integer = 76
5. A family consists of grandparents, parents and three grandchildren. The average age of the grandparents is 67 years that of the parents is 35 years and that of the grandchildren is 6 years. What is the average age of the family?
a) $$28\frac{4}{7}{\text{ years}}$$
b) $$31\frac{5}{7}{\text{ years}}$$
c) $$32\frac{1}{7}{\text{ years}}$$
d) None of these
Explanation: Required average
$$\eqalign{ & {\text{ = }} {\frac{{67 \times 2 + 35 \times 2 + 6 \times 3}}{{2 + 2 + 3}}} \cr & {\text{ = }} {\frac{{134 + 70 + 18}}{7}} \cr & = \frac{{222}}{7} \cr & = 31\frac{5}{7}{\text{ years}} \cr} $$
6. The average age of seven boys sitting in a row facing North is 26 years. If the average age of the first three boys is 19 years and the average age of the last three boys is 32 years, what is the age of the boy who is sitting in the middle of the row?
a) 24 years
b) 28 years
c) 29 years
d) 31 years
Explanation: Age of the boy sitting in the middle
= [26 × 7 - (19 × 3 + 32 × 3)]
= (180 + 153) years
= 29 years
7. The average weight of A, B and C is 45 kg. If the average weight of A and B be 40 kg and that of B and C be 43 kg, then the weight of B is:
a) 17 kg
b) 20 kg
c) 26 kg
d) 31 kg
Explanation: Let A, B, C represent their respective weights.
A + B + C = (45 × 3) = 135.....(i)
A + B = (40 × 2) = 80.....(ii)
B + C = (43 × 2) = 86.....(iii)
Adding (ii) and (iii),
A + 2B + C = 166.....(iv)
Subtracting (i) from (iv), B = 31
B's weight = 31 kg
8. The average weight of 45 students in a class is 52 kg. Five of them whose average weight is 48 kg leave the class and other 5 students whose average weight is 54 kg join the class. What is the new average weight (in kg) of the class?
a) $$52\frac{1}{3}$$
b) $$52\frac{1}{2}$$
c) $$52\frac{2}{3}$$
d) None of these
Explanation: Sum of the weights of the students after replacement
= [(52 × 45) - (48 × 5) + (54 × 5)] kg
= 2370 kg
New average
= $$\left( {\frac{{2370}}{{45}}} \right)$$ kg
= $$52\frac{2}{3}$$ kg
9. The captain of a cricket team of 11 members is 26 years old and the wicket keeper is 3 years older. If the ages of these two are excluded, the average age of the remaining players is one year less than the average of the whole team. What is the average age of the team?
a) 23 years
b) 24 years
c) 25 years
d) None of these
Explanation: Let the average age of the whole team be x years.
11x - (26 + 29) = 9 (x - 1)
11x - 9x = 46
2x = 46
x = 23
10. A motorist travels to a place 150 km away at an average speed of 50 km/hr and returns at 30 km/ hr. His average speed for the whole journey in km/hr is-
a) 35 km/hr
b) 37 km/hr
c) 37.5 km/hr
d) 40 km/hr
Explanation: Average speed
$$\eqalign{ & = \left( {\frac{{2xy}}{{x + y}}} \right){\text{ km/hr}} \cr & = \left( {\frac{{2 \times 50 \times 30}}{{50 + 30}}} \right){\text{ km/hr}} \cr & = 37.5{\text{ km/hr}} \cr} $$