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91. 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 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?
Then, quantity of petrol in 1 litre mixture = (1000 - x) ml
= 38
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.
= Rs. 10
Coast of 1 litre mixture
= Rs.
= Rs. 28
∴ Additional amount earned by pump-owner
= Rs. (30 - 28)
= Rs. 2
Solution:
Let x ml of kerosene be there in 1 litre mixture.Then, quantity of petrol in 1 litre mixture = (1000 - x) ml
= 38
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.
= Rs. 10
Coast of 1 litre mixture
= Rs.
= Rs. 28
∴ Additional amount earned by pump-owner
= Rs. (30 - 28)
= Rs. 2
92. 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?
Solution:
Average body weight
93. 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-
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
Then, 70% of x = 350 kg
.
Average weight of four heaviest boxes
Average weight of four lightest boxes
∴ Required difference
= (350 - 275)
= 75 kg
Solution:
Weight of first box = 200 kgWeight 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
Then, 70% of x = 350 kg
.
Average weight of four heaviest boxes
Average weight of four lightest boxes
∴ Required difference
= (350 - 275)
= 75 kg
94. 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 ?
Let the required integers be x and x -28
Then, x + (x - 28) = 236 - (83 + 29)
⇒ 2x - 28 = 124
⇒ 2x = 152
⇒ x = 76
Hence, required integer = 76
Solution:
Sum of four integers = 59 × 4 = 236Let the required integers be x and x -28
Then, x + (x - 28) = 236 - (83 + 29)
⇒ 2x - 28 = 124
⇒ 2x = 152
⇒ x = 76
Hence, required integer = 76
95. 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?
Solution:
Required average
96. A person purchase 1 kg of tomatoes from each of the 4 places at the rate of 1 kg, 2 kg, 3 kg, 4 kg per rupee respectively. On an average, he has purchased x kg of tomatoes per rupee. Then the value of x is-
Total Money paid
∴ Required average
Solution:
Total quantity purchased = 4 kgTotal Money paid
∴ Required average
97. Out of 9 persons, 8 persons spent Rs. 30 each for their meals. The ninth one spent Rs. 20 more than the average expenditure of all the nine. The total money spent by all of them was-
Then, 9x = 8 × 30 + (x + 20)
⇒ 9x = x + 260
⇒ 8x = 260
⇒ x = 32.50
∴ Total money spent
= Rs. 9x
= Rs. (9 × 32.50)
= Rs. 292.50
Solution:
Let the average expenditure be Rs. xThen, 9x = 8 × 30 + (x + 20)
⇒ 9x = x + 260
⇒ 8x = 260
⇒ x = 32.50
∴ Total money spent
= Rs. 9x
= Rs. (9 × 32.50)
= Rs. 292.50
98. Of the three numbers, the average of the first and the second is greater than the average of the second and the third by 15. What is the difference between the first and the third of the three numbers?
Then,
Solution:
Let the numbers be x, y and z.Then,
99. The average of runs of a cricket player of 10 innings was 32. How many runs must he make in his next innings so as to increase his average of runs by 4 ?
∴ Required number of runs
= (36 × 11) - (32 × 10)
= 396 - 320
= 76
Solution:
Average after 11 innings = 36∴ Required number of runs
= (36 × 11) - (32 × 10)
= 396 - 320
= 76
100. There are 3 groups of students, each containing 25, 50 and 25 students respectively. The mean marks obtained by the first two groups are 60 and 55. The combined mean of all the three groups is 58. What is the mean of the marks scored by the third group ?
Then,
Solution:
Let the mean marks of the third group be x.Then,
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