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# AVERAGES

#### Average Problem for Exams

1. There are two sections A and B of a class, consisting of 36 and 44 students respectively. If the average weight of section A is 40kg and that of section B is 35kg, find the average weight of the whole class.

Total weight of (36+44) Students=(36×40+44×35)kg=2980kg Therefore average weight of the whole class= (2980/80) kg Therefore average weight=37.25kg.

2. Distance between two stations A and B is 778km. A train covers the journey from A to B at 84km per hour and returns back to A with a uniform speed of 56km per hour. Find the average speed of train during the whole journey.
Solution: required average speed = (2xy/x+y) km/hr
= (2x84x56/84+56) km/hr = (2x84x56/140) km/hr = 67.2km/hr. (M.A.T.2003) 3. A Batsman makes a score of 87 runs in the 17th inning and thus increases his average by 3. Find his average after 17th inning.

3.There were 35 students in a hostel. Due to the admission of 7 new students the expenses of the mess were increased by Rs.42 per day while the average expenditure per head diminished by Re 1. What was the original expenditure of the mess?

Solution: let the original average expenditure be Rs.x. then,
42(x-1)-35x=42
=>7x=84
=>x=12
Therefore original expenditure =Rs.(35 x12)=Rs.420.

4.Nine persons went to a hotel for taking their meals. Eight of them spent Rs.12 each on their meals and the ninth spent Rs.8 more then the average expenditure of all the nine. What was the total money spent by them.

Solution:
Let the average expenditure of all the nine be RS.X Then, 12×8+(X+8)=9X Therefore X=13.
Total money spent =9X=RS.(9 x 13)=Rs.117

5.David obtained 76, 65, 82, 67 and 85 marks (out of 100) in English, mathematics, physics, chemistry and biology. What are his average marks?

Solution: Average= (76+65+82+67+85)/5 =375/5=75 Hence average=75.

6.Find the average of all numbers between 6 and 34 which

are divisible by 5.

Solution: Average= (10+15+20+25+30)/5=100/5=20 Hence average=20.

7. A student was asked to find the arithmetic mean of the numbers
3,11,7,9,15,13,8,19,17,21,14 and x. He found the mean to be 12. What should be the number in place of x?

Ans 7.

8. The average of five numbers is 27. If one number is excluded, the average becomes 25. The excluded number is?

Solution: excluded number = (27×5)-(25×4) =135-100 =35.

9. The average of runs of a cricket player of 10 innings was 32. How many runes must be make in his next innings so as to increase his average of runs by 4?

Solution.

Average after 11 innings=36
Required number of runs = ( 36×11) – (32×10) =396-320 =76.

10. The average weight of A, B and C is 45kg. If the weight of A and B be 40kg and that of B and C is 43kg, then the weight of B is.

Let A,B,C represent their respective weights. Then, we have
A+B+C=(45×3)=135 (i)
A+B=(40×2)=80 (ii)
B+C=(43×2)=86 (iii)
Adding (ii) and (iii) we get: A+2B+C=166 (iv)
Subtracting (i) from (iv) we get B=31
Therefore B’s weight =31kg

11.The average monthly income of P and Q is Rs.5050. the average monthly income of Q and R is Rs. 6250 and the average monthly income of P and R is Rs.5200. the monthly income of P.

Solution: let P, Q and R represent their respective monthly incomes. Then, we have

P+Q=(5050×2)=10100 (i)
Q+R=(6250×2)=12500 (ii)
P+R=(5200×2)=10400 (iii)
Adding (i),(ii) and (iii), we get:2(P+Q+R)=33000 (iv)
Subtracting (ii) from (iv) we get p=4000
Therefore p’s monthly income =Rs.4000

12. The average age of 36 students in a group is 14 years. When teacher’s age is included to it, the average increases by one. What is the teacher’s age in years.

Solution: age of teacher = (37×15-36×14)years
= 51 years.

13. The average monthly salary of 20 employees in an organizations is Rs.1500. if the manager’s salary is added, the average salary increases by 100. What is the manager’s monthly salary.

Solution: manager’s monthly salary = Rs. (1600×21-1500×20)
=Rs. 3600.

14. The average weight of 8 persons increases by 2.5kg when a new person comes in place of one of them weighing 65kg. What might be the weight of the new person?

Solution: total weight increased= (8×2.5) kg=20kg
Weight of new person= (65+20)kg=85kg