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Average
21. A batsman makes a score of 87 runs in the 17th inning and thus increases his average by 3. Find his average after 17th inning.
Then, average after 16th inning = (x – 3).
∴ 16 (x – 3) + 87 = 17x
16x – 48 + 87 = 17x
16x + 39 = 17x
x = 39
22. The batting average for 40 innings of a cricket player is 50 runs. His highest score in an innings exceeds his lowest score by 172 runs. If these two innings are excluded, the average score of the remaining 38 innings is 48 runs. Find his highest score in an innings.
Then, lowest score = (x – 172).
x + (x – 172) = 50 × 40 – 48 × 38
2x – 172 = 2000 – 1824
2x – 172 = 176
2x = 348
x = 174
23. 10 years ago, the average age of a family of 4 members was 24 years. Since then, two children having been born, still the average age of the family is the same today. If the two children differ in age by 2 years, find the present age of the younger child.
Total age of 4 members now = 96 + (10 × 4) = 136 years.
Total age of 6 members now = 24 × 6 = 144 years.
Sum of ages of 2 children = 144 – 136 = 8 years.
Let age of younger child = x.
x + (x + 2) = 8
2x + 2 = 8
2x = 6
x = 3 years
24. Distance between two stations A and B is 778 km. A train covers the journey from A to B at 84 km per hour and returns back to A with a uniform speed of 56 km per hour. Find the average speed of the train during the whole journey.
= (2 × 84 × 56) / (84 + 56)
= (2 × 84 × 56) / 140
= 67.2 km/hr
25. The average salary of workers of a factory is ₹ 6000, while the average salary of 150 technicians is ₹ 12000 and that of non-technicians is ₹ 3750. Find the total number of workers in the factory.
6000x = (12000 × 150) + 3750 (x – 150)
6000x = 1800000 + 3750x – 562500
2250x = 1237500
x = 550
26. The average score of girls in class X examination in a school is 73 and that of boys is 71. The average score in class X of that school is 71.8. Find the percentage of the number of girls and boys in class X of the school.
71x + 73y = 71.8 (x + y)
0.8x = 1.2y
x = 3/2 y
Percentage of boys = 60%
Percentage of girls = 40%
27. 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 the 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.
Third box = 250 kg.
Second box = 300 kg.
Fourth box = 350 kg.
Fifth box = 500 kg.
Average of four heaviest = 350 kg.
Average of four lightest = 275 kg.
Difference = 75 kg.
28. In Arun’s opinion, his weight is greater than 65 kg but less than 72 kg. His brother does not agree with Arun and he thinks that Arun’s weight is greater than 60 kg but less than 70 kg. His mother’s view is that his weight cannot be greater than 68 kg. If all of them are correct in their estimation, what is the average of different probable weights of Arun?
Average = (66 + 67 + 68) / 3 = 67 kg
29. 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?
= 222 / 7
= 315 / 7 years
30. Out of 9 persons, 8 persons spent ₹ 30 each for their meals. The ninth one spent ₹20 more than the average expenditure of all the nine. The total money spent by all of them was.
9x = 8 × 30 + (x + 20)
8x = 260
x = 32.50
Total money spent = 9 × 32.50 = ₹292.50
