Average

Given, Mean monthly salary of 75 workers = ₹5680
⇒ Total monthly salary of 75 workers = 5680 × 75 = ₹ 4,26,000
Given, Mean salary of 25 of them = ₹5400
⇒ Total monthly salary of 25 workers = 5400 × 25 = ₹ 1,35,000
Given, Mean salary of 30 others = ₹5700
⇒ Total monthly salary of 30 other workers = 5700 × 30 = ₹ 1,71,000
Now, Total salary of the remaining workers (i.e., 20 other workers) = Total monthly salary of 75 workers - (Total monthly salary of 25 workers + Total monthly salary of 30 other workers)
= 4,26,000 - (1,35,000 + 1,71,000)
= 4,26,000 - 3,06,000
= 1,20,000
Average salary of the remaining workers (i.e., 20 other workers) = 1,20,000/20
= ₹ 6000

Total quantity of petrol consumed in 3 years = (4000/7.50 + 4000/8 + 4000/8.50) liters
= 4000 (100/750 + 1/8 + 100/850)
= 4000 (2/15 + 1/8 + 2/17)
= 4000 [(272 + 255 + 240)/2040]
= 4000 [767/2040]
= 76700/51 liters
Total amount spent in 3 years = ₹ 4000 × 3 = ₹ 12000.
Average cost per litre of petrol for 3 years = Total amount spent in 3 years / Total quantity of petrol consumed in 3 years
= ₹ (12000×51/76700)
= 120×51 / 767
= 6120/767
= ₹ 7.98

⇒ Sum of eight numbers = 25 × 8 = 200
⇒ Sum of first two numbers = (39/2) × 2 = 39
⇒ Sum of first three numbers = (70/3) × 3 = 70
⇒ Let, the sixth number be x
⇒ So, sum of sixth, seventh and eighth number = 200 – (39+70) = 200 – 109 = 91
⇒ = x+x+5+x+8 = 91
⇒ =×= 26
⇒ ∴ seventh number = 26 + 5 = 31
⇒ So option (a) is the correct answer:

Given
The family consists of two grandparents, two parents and three grandchildren
The average age of two grandparents = 67 years.
⇒ Total age of two grandparents = (67 × 2) = 134 years
The average age of two parents = 35 years
⇒ Total age of two parents = (35 × 2) = 70 years
The average age of three grand children = 6 years.
⇒ Total age of three grand children = (6 × 3) = 18 years.
Required Average age of the family = Total age of (two grandparents + two parents + three grand children) / Total members in the family
= ( 134 + 70 + 18 ) / (2 + 2 + 3)
= 222 / 7
= 31 (5 / 7) years

Ratio of number of boys and number of girls = 1.2 : 0.8
= 12 : 8
= 3 : 2.

The average age of a group of 10 students is 18.
∴ the sum of the ages of all 10 of them = 10 × 18 = 180
When two students joins the group, the average increase by 1. New Average = 19
Now there are 12 students ∴ sum of all the ages of 12 students = 12 X 19 = 228
∴ the sum of the ages of two students who joined = 228 - 180 = 48
And the average age of these two students = 24

The average age of a group of 10 students is 12.
∴ the sum of the ages of all 10 of them = 10 × 12 = 120
When two students joins the group, the average increase by 2.
New Average = 14 Now there are 12 students
∴ sum of all the ages of 12 students = 168
∴ the sum of the ages of two students who joined = 168 - 120 = 48
And the average age of these two students = 24

The average age of a group of 10 students is 10.
∴ the sum of the ages of all 10 of them = 10 × 10 = 100
When two students joins the group, the average increase by 1.
⇒ New Average = 11
Now there are 12 students.
∴ sum of all the ages of 12 students = 11×12 = 132
∴ the sum of the ages of two students who joined = 132 - 100 = 32
And the average age of these two students = (32 / 2) = 16

The average age of a group of 10 students is 16.
∴ the sum of the ages of all 10 of them
= 10 × 16 = 160
When two students joins the group, the average increase by 2.
New Average = 18
Now there are 12 students
∴ sum of all the ages of 12 students = 216
∴ the sum of the ages of two students who joined
= 216 - 160 = 56
And the average age of these two students
= 56 / 2
= 28:

The average age of a group of 10 students is 20. ∴ the sum of the ages of all 10 of them = 10 × 20 = 200 When two students joins the group, the average increase by 2. New Average = 22 Now there are 12 students ∴ sum of all the ages of 12 students = 264 ∴ the sum of the ages of two students who joined = 264 - 200 = 64 And the average age of these two students = 32