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Different type of problem of Average

Problems related to Batting/Bowling:

Before discussing the problem remember that,

Batting average = (Runs / Innings)

Bowling average = (Runs / Wicket)

(Q1): Batting average of a batsman after 20 innings was 47. In the 21st innings, he scored a few runs. For that, his average was increased by 3. Then how much run he scored in the 21st innings.

Solution:

(i) Traditional:

Runs after 20 innings = 20 * 47 = 940

Runs after 21 innings = 21 * 50 = 1050

Runs in 21 innings is = (1050 - 940) = 110

(ii) Shortcut method:

Average run increased by 3.

So, runs in 21 innings = 47 + (21*3) = 47 + 63 = 110

(Q2): A batsman in his 16th innings makes a score of 112 and thereby increases his average by 4 runs. What is the average after 16th innings?

Solution:

(i) Traditional:

Let the average after 15th innings be x

Then total runs after the 15th innings are15x

In the 16th innings, he scores 112 runs

So, 15x + 112 = 16(x+4)

→ 15x + 112 = 16x +64

→ x = 112 - 64 = 48

So, the average after the 16th innings is (48+4) = 52 

(ii) Shortcut method:

Average after 15th innings = 112 - (16 * 4) = 48

Average after 16th innings = 112 – 4(16-1) = 52 

Problems related to Average Speed and Time:

We know speed = (Total distance/ Total Time)

Now,

Case (1):

When the distance traveled in different time slots and parts is the same.

Suppose a man covers x km distance at a km/ hour speed. And another x km distance at b km/ hour speed.

Case (2):

If in the total journey there are 3 parts of distance x km with 3 different speeds.

Suppose a person covers the first x km at a speed of a km/hr, the next x km at a speed of b km/hr, and the last x km at a speed of c km/hr. 

(Q1): Ram goes to Kolkata to Delhi at the speed of 40km/hr and return at the speed of 60km/hr. Then find the average speed of Ram during the whole journey.

Solution:

Now distance is same,

So the average speed of the whole journey is

(Q2): Trilok travels (1/3)rd of the total distance at the speed of 10km/hr and next (1/3)rd at the speed of 20km/hr. And last (1/3)rd at the speed of 60km/hr.

Solution:

(Q3): A person covers half of the distance at 20km/hr and the half of the remaining distance 40km/hr and the rest 60km/hr. Find the average speed during the journey.

Solution: 

Let the total distance be x km.

A person covers half of the distance at 20km/hr.

So, the time to complete the (x/2) km is (x/40) hr.

A person covers half of the remaining distance at 40km/hr,

So, the time to complete the (x/4) km is (x/160) hr

A person covers rest distance at 60km/hr

So, the time to complete the (x/4) km is (x/240) hr

We know average speed = (Total Distance / Total time)

Problems on Weighted Average:

Then,

(Q1): In a collage there are three departments Mechanical, Electrical, MBA. Total students in these 3 departments are 15, 30, 10 respectively. And their respective ages (in years) are 25, 26, 33. Then find the average ages of all the students.

Solution:

Miscellaneous problems:

(Q1): The average of six numbers is 50. If the average of the first 3 numbers is 45 and the last four is 55. Then find the third number?

Solution:

The average of six numbers is 50

Sum of six number is (50 * 6) = 300

The average of the first three numbers is 45

Sum of three number is (45 * 3) = 135

The average of the last four numbers is 55

Sum of last four number is (55 * 4) = 220

So, the third number is (220 + 135 - 300) = 55

(Q2): The average of 10 numbers is 45. The average of the first five is 40, and the average of the last four is 48. Find the 5th number.

Solution:

The average of ten numbers is 45

Sum of ten numbers is (45 * 10) = 450

The average of the first five numbers is 40

So, the Sum of the first five numbers is (40 * 5) = 200

The average of the last four numbers is 48

So, the Sum of the last four numbers is (48 * 4) = 192

Sum of first five numbers and last four numbers is (200 + 192) = 392

So, the 5th number is (450 - 392) = 58

(Q3): The average temperature on Monday, Tuesday, and, Wednesday is 35°c. The average temperature on Tuesday, Wednesday, Thursday is 41°c. If the average temperature on Monday and Thursday is 25°c. Then find the temperature on Monday and Thursday?

Solution:

M + T + W = 35 * 3 = 105 ----- (i)

T + W + Th = 41 * 3 = 123 ----- (ii)

Now, from (ii) - (i) we get

Th – M = 18 ----- (iii)

Th + M = 25 * 2 = 50 ----- (iv)

Now solving (iii) and (iv) we get,

Th = (50 + 18)/2

     = 34

M = 16

So, the temperature of Monday is 16°c.

The temperature of Thursday is 34°c.