Practice Test: Averages - 2 - UPSC MCQ

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.

As, Mean = Total Sum of Observations / No. of Observations

Clearly, we have (3 + 11 + 7 + 9 + 15 + 13 + 8 + 19 + 17 + 21 + 14 + x) / 12 = 12.

or  137 + x = 144

⇒ x = 144 - 137 = 7.

Average = (76 + 65 + 82 + 67 + 85 )/ 5 = 375/5 =  75.