# Averages Part 7

Problem 1: A cricket player after playing 10 tests scored 100 runs in the 11th test. As a result, the average of his runs is increased by 5. The present average of runs is?

Solution:

Average for 11 tests =100

Average = 5

Average+number*increment = Total

a+11*5=100

a=100-55=45

Shortcut:

a=100-11*5=45

N=a+5=45+5=50

Problem 2: The average age of 20 boys is 14 years. A boy who is 16 years old left them and one new boy replaces him. Then the average becomes 13.8 years. Find the age of the new boy?

Solution:

20*14 – 16+a= 13.8*20

280-16+a=276

a = 276-264 = 12

Shortcut:

16-0.2*20=12

Problem 3: The average temperature of Monday, Tuesday and Wednesday was $30^{\circ}C$ and that of Tuesday, Wednesday and Thursday was $33^{\circ}C$. If the temperature on Monday was $32^{\circ}C$, then the temperature on Thursday was?

Solution:

T+W+TH = 33*3

M+T+W=30*3

TH-32=9

TH = 32+9 =41