Problems on Averages - Aptitude Questions and Answers Part 2

6. Rajesh Shopping Bill looks like this:

Item (Qty)Price/ unit
----------------
Pencils (35)Rs 4/-
Pens (30)Rs 11/-
Sharpeners (25)Rs 3/-

Find the average price of the goods he has bought.   

a. Rs. 5.5
b. Rs. 6.05
c. Rs. 8.25
d. Rs. 9

Answer: b. Rs. 6.05

Explanation:

Average=Sum of Observations
Number of Observations


Average=Total cost of pencils + Total cost of pens + Total cost of sharpeners
Total pencils + Total pens + Total sharpeners

∴ Average price =(35 x 4)+(30 x 11)+(25 x 3)=Rs. 6.05
35+30+25


7. Rakshit sold 21 tables in a day. He told his father, "My earnings at end of the day are Rs 400000/-. The average earning from the first 11 tables I sold was Rs 20000/-". What were his average earnings from the remaining tables?

a. Rs. 9125
b. Rs. 9750
c. Rs. 16,363
d. Rs. 18,000

Answer: d. Rs. 18,000

Explanation:

Average=Sum of Observations
Number of Observations


Total earnings from all 21 tables = Rs. 400000

Total cost of 11 tables = Average cost of 11 tables  x 11 tables = 20000 x 11

Cost of remaining (21-11=10) tables = 400000 - (20000 x 11) = Rs. 180000

Average of remaining 10 tables=180000=Rs. 18,000/-
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8. If I do not consider the earnings from selling the six seater dining table, my average falls by Rs 2000/-. What is the cost of six seater dining table if average earnings from selling 11 four seater dining tables and one six seater dining table is Rs 18000?

a. Rs. 29000
b. Rs. 30000
c. Rs. 36000
d. Rs. 40000

Answer: d. Rs. 40000

Explanation:

Without six seater dining table, there are 11 four seater dining tables.

Average = 18000 - 2000 = 16000.

Total cost of 11 small dining tables = 11 x 16000 = Rs. 176000

With big dining table, total cost of 12 tables = 12 x 18000 = Rs. 216000

Cost of six seater dining table = 216000 - 176000 = Rs. 40000


9. The cargo ship was carrying gas cylinders from Australia to New Zealand. 3 cylinders with average weight X Kg belonged to a single owner. Last minute one of the cylinders weighing 85 kg was replaced by another cylinder leading to a rise in average weight of the 3 cylinders by 7 kg. Find the weight of the new cylinder.
  
a. 79 kg
b. 92 kg
c. 106 kg
d. 109 kg

Answer: c. 106 kg

Explanation:

Since increase in average is by 7 kg, weight of each cylinder would increase by 7 kg.

So total increase in weight = 7kg x 3 cylinders = 21 kg.

So weight of new cylinder needs to be = 85 + 21 = 106 kg.

Remember:
We may think that weight should be 85 + 7 = 92 kg.
But it is 106 kg → because the new cylinder must include the increase in weight for other 2 cylinders too. So 7kg + 7kg of other two cylinders must be added in new cylinder.


10. In an exam, the average marks for 80 students of Class V is 35. The average of marks in section A of the class is 55 while the average of marks in section B is 30. Find the number of students in Class V B.

a. 45
b. 50
c. 64
d. 70

Answer: c. 64

Explanation:

Total students i.e. Section A + Section B = 80

Section A = 80 - Section B = 80 - B

∴ 80 x 35 = B x 30 + (80 - B) x 55

2800 = 30B + 4400 - 55B  

1600 = 25 B

B = 64

∴ B = 64 = Number of students in Class V B.

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