Averages - 2 - UPSC Free MCQ Practice Test with solutions

Total sale for 5 months = Rs. (6435 + 6927 + 6855 + 7230 + 6562) = Rs. 34009.

 Required sale = Rs. [ (6500 x 6) - 34009 ]

   = Rs. (39000 - 34009)

   = Rs. 4991.

Let A, B, C represent their respective weights. Then, we have:

A + B + C = (45 x 3) = 135 .... (i)

A + B = (40 x 2) = 80 .... (ii)

B + C = (43 x 2) = 86 ....(iii)

Adding (ii) and (iii), we get: A + 2B + C = 166 .... (iv)

Subtracting (i) from (iv), we get : B = 31.

 B's weight = 31 kg.

Sum of the present ages of husband, wife and child = (27 * 3 + 3 * 3) years = 90 years.
Sum of the present ages of wife and child = (20 * 2 + 5 * 2) years = 50 years.
Husband's present age = (90 - 50) years 
= 40 years

The average weight of 8 persons increases by 2.5 kg
Total weight of 8 persons increased = 8 × 2.5 kg = 20 kg.
New person comes in place of one of them weighing 65 kg.
Hence the increase of weight of 8 persons together is because of new person replacing the person having 65 kg weight. Accordingly
Weight of new person = 65 + 20 kg = 85 kg
Thus the person replacing the 65 kg person should have 85 kg weight, which causes increase of weight of the group together by 2.5 kg .

Weighted Average=[(Weight of Group 1) * (Average of Group 1) + (Weight of Group 2) * (Average of Group 2)]/Total Weight

In this case, Group 1 is Division A and Group 2 is Division B.

Given information:

• Weight of Division A (Weight of Group 1Weight of Group 1) = 36 students
• Average weight of Division A (Average of Group 1Average of Group 1) = 40 kg
• Weight of Division B (Weight of Group 2Weight of Group 2) = 44 students
• Average weight of Division B (Average of Group 2Average of Group 2) = 35 kg

Now, plug these values into the formula:

Weighted Average=[(36 students×40 kg)+(44 students×35 kg)]/36+44

Weighted Average=37.25kg

So, the average weight of the whole class is 37.25 kg.

Let the batsman’s average after 16 innings be x.
When he scores 87 in the 17th inning, his total runs become 16x + 87.
Since his average increases by 3 after the 17th inning, his new average is x + 3.
Using this information, we can set up the equation:
(16x + 87) / 17 = x + 3
Now we can solve for x:
16x + 87 = 17(x + 3)
16x + 87 = 17x + 51
87 - 51 = 17x - 16x
36 = x
So, the batsman's average after 16 innings was x = 36. Since his average increased by 3, his new average after the
17th inning is:
36 + 3 = 39
Answer:
The correct answer is (a) 39.

There are 12 numbers in total, and the arithmetic mean is 12. This means the total sum of the numbers is 12 × 12 = 144.

Now, add the given numbers: 3 + 11 + 7 + 9 + 15 + 13 + 8 + 19 + 17 + 21 + 14 = 137.

Since the sum including x must equal 144, we have: 137 + x = 144
x = 144 − 137
x = 7

The average mark is calculated by adding all the marks together and dividing by the number of subjects.

• Average = (76 + 65 + 82 + 67 + 85) / 5
• Sum of marks = 76 + 65 + 82 + 67 + 85 = 375
• Number of subjects = 5
• Average = 375 / 5 = 75

Thus, Arun's average mark is 75.