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51. 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?
⇒ 7x = 84
⇒ x = 12
Therefore original expenditure,
= Rs. (35 × 12)
= Rs. 420
Solution:
Let the original average expenditure be Rs. x then,42(x - 1) - 35x = 42⇒ 7x = 84
⇒ x = 12
Therefore original expenditure,
= Rs. (35 × 12)
= Rs. 420
52. 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.
Then, 12 × 8 + (x + 8) = 9x
Therefore, x = 13
Total money spent,
= 9x
= Rs. (9 × 13)
= Rs. 117
Solution:
Let the average expenditure of all the nine be xThen, 12 × 8 + (x + 8) = 9x
Therefore, x = 13
Total money spent,
= 9x
= Rs. (9 × 13)
= Rs. 117
53. David obtained 76, 65, 82, 67 and 85 marks (out of 100) in English, mathematics, physics, chemistry and biology. What are his average marks?
Solution:
54. 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?
Required number of runs,
= ( 36 × 11) - (32 × 10)
= 396 - 320
= 76
Solution:
Average after 11 innings = 36Required number of runs,
= ( 36 × 11) - (32 × 10)
= 396 - 320
= 76
55. 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.
= (36 × 40 + 44 × 35) kg
= 2980 kg
Therefore average weight of the whole class,
= kg.
Therefore average weight = 37.25 kg.
Solution:
Total weight of (36 + 44) Students,= (36 × 40 + 44 × 35) kg
= 2980 kg
Therefore average weight of the whole class,
= kg.
Therefore average weight = 37.25 kg.
56. Distance between two stations A and B is 778km. A train covers the journey from A to B at 84km per hour and returns back to A with a uniform speed of 56km per hour. Find the average speed of train during the whole journey.
Solution:
57. The average of 50 numbers is 30. If two numbers, 35 and 40 are discarded, then the average of the remaining numbers is nearly:
= (50 × 30) - (35 + 40)
= 1500 - 75
= 1425
Average = = 29.68
Solution:
Total sum of 48 numbers,= (50 × 30) - (35 + 40)
= 1500 - 75
= 1425
Average = = 29.68
58. The average score of a cricketer for ten matches is 38.9 runs. If the average for the first six matches is 42, then find the average for the last four matches.
= (10 × 38.9) - (6 × 42)
= 389 - 252 = 137
Average = = 34.25
Solution:
Total sum of last 4 matches, = (10 × 38.9) - (6 × 42)
= 389 - 252 = 137
Average = = 34.25
59. 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.
Then, 12 × 8 + (X + 8) = 9X
∴ X = 13Total money spent = 9X
= Rs. (9 × 13)
= Rs. 117
Solution:
Let the average expenditure of all the nine be Rs. XThen, 12 × 8 + (X + 8) = 9X
∴ X = 13Total money spent = 9X
= Rs. (9 × 13)
= Rs. 117
60. 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?
Required number of runs
= ( 36 × 11) - (32 × 10)
= 396 - 320
= 76
Solution:
Average after 11 innings = 36Required number of runs
= ( 36 × 11) - (32 × 10)
= 396 - 320
= 76