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61. The average wages of a worker during a fortnight comprising 15 consecutive working days was Rs.90 per day. During the first 7 days, his average wages was Rs.87/day and the average wages during the last 7 days was Rs.92 /day. What was his wage on the 8th day?
= 15 × 90
= Rs. 1350
The total wages earned during the first 7 days
= 7 × 87
= Rs. 609
The total wages earned during the last 7 days
= 7 × 92
= Rs. 644
Total wages earned during the 15 days,
= wages during first 7 days + wage on 8th day + wages during the last 7 days.
1350 = 609 + wage on 8th day + 644
wage on 8th day = 1350 - 609 - 644 = Rs. 97
Solution:
The total wages earned during the 15 days that the worker worked ,= 15 × 90
= Rs. 1350
The total wages earned during the first 7 days
= 7 × 87
= Rs. 609
The total wages earned during the last 7 days
= 7 × 92
= Rs. 644
Total wages earned during the 15 days,
= wages during first 7 days + wage on 8th day + wages during the last 7 days.
1350 = 609 + wage on 8th day + 644
wage on 8th day = 1350 - 609 - 644 = Rs. 97
62. The average temperature on Wednesday, Thursday and Friday was 25°. The average temperature on Thursday, Friday and Saturday was 24°. If the temperature on Saturday was 27°, what was the temperature on Wednesday?
Total temperature on Thursday, Friday and Saturday was 24 × 3 = 72°
Hence, difference between the temperature on Wednesday and Saturday = 3°
If Saturday temperature =27°, then
Wednesday's temperature = 27 + 3 = 30°
Solution:
Total temperature on Wednesday, Thursday and Friday was 25 × 3 = 75°Total temperature on Thursday, Friday and Saturday was 24 × 3 = 72°
Hence, difference between the temperature on Wednesday and Saturday = 3°
If Saturday temperature =27°, then
Wednesday's temperature = 27 + 3 = 30°
63. When a student weighing 45 kgs left a class, the average weight of the remaining 59 students increased by 200g. What is the average weight of the remaining 59 students?
The questions states that when the weight of this student who left is added, the total weight of the class = 59X + 45
When this student is also included, the average weight decreases by 0.2 kgs
59X + = X - 0.2
=> 59X + 45 = 60X - 12
=> 45 + 12 = 60X - 59X
=> X = 57
Solution:
Let the average weight of the 59 students be XTherefore, the total weight of the 59 of them will be 59XThe questions states that when the weight of this student who left is added, the total weight of the class = 59X + 45
When this student is also included, the average weight decreases by 0.2 kgs
59X + = X - 0.2
=> 59X + 45 = 60X - 12
=> 45 + 12 = 60X - 59X
=> X = 57
64. The difference between two angles of a triangle is 24°. The average of the same two angles is 54°. Which one of the following is the value of the greatest angle of the triangle?
⇒ a – b = 24
Since the average of the two angles is 54°, we have = 54
Solving for b in the first equation yields b = a – 24, and substituting this into the second equation yields,
2a − 24 = 54 × 2
2a − 24 = 108
2a = 108 + 24
2a = 132
a = 66
Also,
b = a − 24 = 66 − 24 = 42
Now, let c be the third angle of the triangle. Since the sum of the angles in the triangle is
180°, a + b + c = 180°
Putting the previous results into the equation yields 66 + 42 + c = 180°
Solving for c yields c = 72°
Hence, the greatest of the three angles a, b and c is c, which equal.
Solution:
Let a and b be the two angles in the question, with a > b. We are given that the difference between the angles is 24°.⇒ a – b = 24
Since the average of the two angles is 54°, we have = 54
Solving for b in the first equation yields b = a – 24, and substituting this into the second equation yields,
2a − 24 = 54 × 2
2a − 24 = 108
2a = 108 + 24
2a = 132
a = 66
Also,
b = a − 24 = 66 − 24 = 42
Now, let c be the third angle of the triangle. Since the sum of the angles in the triangle is
180°, a + b + c = 180°
Putting the previous results into the equation yields 66 + 42 + c = 180°
Solving for c yields c = 72°
Hence, the greatest of the three angles a, b and c is c, which equal.
65. The average age of a family of 5 members is 20 years. If the age of the youngest member be 10 years then what was the average age of the family at the time of the birth of the youngest member?
The total age of the family at the time of the birth of the youngest member,
= 100 - 10 - (10 × 4)
= 50
Therefore, average age of the family at the time of birth of the youngest member,
Solution:
At present the total age of the family = 5 × 20 =100The total age of the family at the time of the birth of the youngest member,
= 100 - 10 - (10 × 4)
= 50
Therefore, average age of the family at the time of birth of the youngest member,
66. Which one of the following numbers can be removed from the set S = {0, 2, 4, 5, 9} without changing the average of set S?
If we remove an element that equals the average, then the average of the new set will remain unchanged. The new set after removing 4 is {0, 2, 5, 9}.
The average of the elements is,
Solution:
The average of the elements in the original set S is:If we remove an element that equals the average, then the average of the new set will remain unchanged. The new set after removing 4 is {0, 2, 5, 9}.
The average of the elements is,
67. Average cost of 5 apples and 4 mangoes is Rs. 36. The average cost of 7 apples and 8 mangoes is Rs. 48. Find the total cost of 24 apples and 24 mangoes.
Total cost = 36 × 9 = 324
Average cost of 7 apples and 8 mangoes = 48
Total cost = 48 × 15 = 720
Total cost of 12 apples and 12 mangoes = 324 + 720 = 1044
Therefore, cost of 24 apples and 24 mangoes = 1044 × 2 = 2088
Solution:
Average cost of 5 apples and 4 mangoes = Rs. 36Total cost = 36 × 9 = 324
Average cost of 7 apples and 8 mangoes = 48
Total cost = 48 × 15 = 720
Total cost of 12 apples and 12 mangoes = 324 + 720 = 1044
Therefore, cost of 24 apples and 24 mangoes = 1044 × 2 = 2088
68. The average weight of three boys A, B and C is kg, while the average weight of three boys B, D and E is 53 kg. What is the average weight of A, B, C, D and E?
Therefore the answer is Data inadequate.
Solution:
In this question, sum of numbers is provided, net required sum (i.e. A + B+ C+ D + E) cannot be calculated by the given data.Therefore the answer is Data inadequate.
69. Average of ten positive numbers is x. If each number is increased by 10%, then x :
According to question average of these 10 numbers is 10
Now if each number is increased by 10%,
then new average, say y.
Solution:
Let 10 numbers be x1, x2, x3, . . . . . . . x10According to question average of these 10 numbers is 10
Now if each number is increased by 10%,
then new average, say y.
70. The average price of 10 books is Rs.12 while the average price of 8 of these books is Rs. 11.75. Of the remaining two books, if the price of one book is 60% more than the price of the other, what is the price of each of these two books?
Total cost of 8 books = Rs. 94
⇒ The cost of 2 books = Rs. 26
Let the price of each book be x and y.
⇒ x + y = 26 - - - - - -(1)
Given that the price of 1 book is 60% more than the other price
Solution:
Total cost of 10 books = Rs. 120Total cost of 8 books = Rs. 94
⇒ The cost of 2 books = Rs. 26
Let the price of each book be x and y.
⇒ x + y = 26 - - - - - -(1)
Given that the price of 1 book is 60% more than the other price