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Shortcuts and Tricks in Averages – Quant without pen

Question 1:
The average age of the district level hockey team of eleven is 22 years.The average age gets increased by 1 year when the coach age is also included.what is the age of the coach ?
A) 33 yrs B) 34 yrs C) 35 yrs D) 36 yrs
Question 2:
The average weight of a class of 24 students is 35 kg. If the weight of the teacher be included, the average rises by 400 g. The weight of the teacher is :
A) 45 kg B) 46 kg C) 47 kg D) 48 kg
Question 3:
20 men went to a restaurant. Ninteen of them paid Rs.70 each and the twentieth man paid Rs.90.25 more than the average of all the 20 men. What is the total bill ?
A) Rs. 1495 B) Rs. 548 C) Rs. 850 D) Rs. 1750
Question 4:
A batsman scores 26 runs and increases his average from 14 to 15. Find the runs to be made if he wants top increasing the average to 19 in the same match ?
A) 74 B) 79 C) 72 D) 60
Question 5:
There are 44 students in a hostel, due to the administration, 15 new students has joined. The expense of the mess increase by Rs. 33 per day. While the average expenditure per head diminished by Rs. 3, what was the original expenditure of the mess ?
A) Rs. 404 B) Rs. 514 C) Rs. 340 D) Rs. 616
Explanation:
Weight of the teacher = (35.4 x 25 – 35 x 24) kg = 45 kg.
Explanation:
Total age of players in team = 22 x 11 = 242
When coach is included, total members = 12, Avg age increases by one becomes 23
Total age when coach is included = 23×12 = 276
Age of coach = 276-242 = 34 yrs.
Explanation:
Let the average bill paid by twenty members = ‘x’
But 19 men paid each = Rs. 70
20th man paid Rs. 90.25 more than the avg bill of 20 = x + 90.25
20x = 19(70) + x + 90.25
19x = 1330 + 90.25
19x = 1420.25
x = 1420.25/19 = Rs. 74.75
But the total bill = 20 x 74.75 = A) Rs. 1495
Explanation:
Number of runs scored more to increse the ratio by 1 is 26 – 14 = 12
To raise the average by one (from 14 to 15), he scored 12 more than the existing average.
Therefore, to raise the average by five (from 14 to 19), he should score 12 x 5 = 60 more than the existing average. Thus he should score 14 + 60 = 74. A) 74
Explanation:
Let the average expenditure per head be Rs. p
Now, the expenditure of the mess for old students is Rs. 44p
After joining of 15 more students, the average expenditure per head is decreased by Rs. 3 => p-3
Here, given the expenditure of the mess for (44+15 = 59) students is increased by Rs. 33
Therefore, 59(p-3) = 44p + 33
59p – 177 = 44p + 33 => 15p = 210 => => p = 14
Thus, the expenditure of the mess for old students is Rs. 44p = 44 x 14 = Rs. 616.
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