Hi friends,

Average is an important topic as it is not only used to solve direct questions, but also can be used to solve other questions. Therefore for such an important topic, Team SSCHacks is here with the easiest and the most efficient tricks to find out the average quickly in different questions whenever asked or needed in the SSC CGL 2017 exam.

Please follow the following rules and there examples:

Rule 1:

If different distance is traveled in different time then,

Description: D:\Site Articles\Average\with example\final\images\average-shortcut-methods-1-1_cr.png

Example:
If a car travels 50 Km in 1 hour, another 40 Km in 2 hour and another 70 Km in 3 hour then what is average speed of car.

Sol:
Description: D:\Site Articles\Average\with example\final\images\average-shortcut-methods-1-1_cr.png
Total Distance Covered = 50 + 40 + 70 = 160 Km
Total Time Taken = 1 + 2 + 3 = 6 hours.
Description: D:\Site Articles\Average\with example\final\images\average-shortcut-methods-1-2_cr.png

Rule 2:

If equal distance is traveled at different speed.

If equal distance is traveled at the speed of A and B then,

Description: D:\Site Articles\Average\with example\final\images\average-shortcut-methods-1-3_cr.png

Example:
A boy goes to his school which is 2 Km away in 10 minutes and returns in 20 mins then what is boy’s average speed.

Sol:
Description: D:\Site Articles\Average\with example\final\images\average-shortcut-methods-1-3_cr.png
Let’s say A = 2/10 = 0.2 km/min
And B = 2/20 = 0.1 km/min
Description: D:\Site Articles\Average\with example\final\images\average-shortcut-methods-1-4_cr.png

Rule 3:

If equal distance is traveled at the speed of A, B and C then,

Description: D:\Site Articles\Average\with example\final\images\average-shortcut-methods-1-5_cr.png

Example:

If a car divides its total journey in three equal parts and travels those distances at speed of 60 kmph, 40 kmph and 80 kmph then what is car’s average speed?

Sol:Description: D:\Site Articles\Average\with example\final\images\average-shortcut-methods-1-5_cr.png

Let’s say A = 60, B = 40 and C = 80, then

Description: D:\Site Articles\Average\with example\final\images\average-shortcut-methods-1-6_cr.png

                        Description: D:\Site Articles\Average\with example\final\images\average-shortcut-methods-1-7_cr.png

When a person leaves the group and another person joins the group in place of that person then:

Rule 1:

If the average age is increased,

Age of new person = Age of separated person + (Increase in average × total number of persons)

Example:
The average age of 10 persons is increased by 5 years when one member of age 40 years is replaced by a new person. What is age of new person?

Sol: Age of new person = Age of separated person + (Increase in average × total number of persons)Age of separated person

= 40 Increase in average = 5 Total number of persons = 10 Age of new person = 40 + ( 5 × 10 ) = 40 + 50 = 90 years.

Rule 2:

If the average age is decreased,

Age of new person = Age of separated person – (Decrease in average × total number of persons)

Example:
Average age of 20 persons is decreased by 1 year when a person aged 25 years is replaced by a new person. What is age of new person?

Sol:Age of new person = Age of separated person – (Decrease in average × total number of persons)Age of separated person

= 25 years Decrease in average = 1  year Age of new person

= 25 – (1 × 20) = 25 – 20 = 5 years.

Rule 3:

New average age of group =

Description: D:\Site Articles\Average\with example\final\images\average-shortcut-methods-2-1.png

Example:

A group of 10 persons has an average age of 25 years. A person of that group aged 20 years is replaced by a new person aged 30 years. What is new average of the group?

Sol:  New average age of group =

Description: D:\Site Articles\Average\with example\final\images\average-shortcut-methods-2-1.pngPrevious average = 25 years Number of persons = 10 Age of leaving person = 20 Age of joining person = 30Description: D:\Site Articles\Average\with example\final\images\average-shortcut-methods-2-2_cr.png

New Average when a person joins the group.

Rule 1:

In case of increase in average Age of new member = Previous average + ( Increase in average × Number of members including new member)

Example:
The average age of 15 boys is 17 years and is increased by 0.5 years when a new boy is joined in the group. What is the average of new boy?

Sol:Age of new member = Previous average + ( Increase in average × Number of members including new member)Previous average

= 17 years Increase in average = 0.5 years Number of members including new member

= 16  

So,Age of new member = 17 + ( 0.5 × 16) = 17 + 8 = 25 years.

Rule 2:

In case of decrease in average Age of new member = Previous average – ( Decrease in average × Number of members including new member)

Example:
The average age of 10 girls is 23 years and is decreased by 0.5 years when a new girl is joined in the group. What is the age of new girl?

Sol:Age of new member = Previous average – ( Decrease in average × Number of members including new member)Previous average

= 23 years Decrease in average = 0.5 years Number of members including new member

= 11 Age of new member = 23 – ( 0.5 × 11) = 23 – 5.5 = 17.5 years

Rule 3:

New average of group =

Description: D:\Site Articles\Average\with example\final\images\average-shortcut-methods-3-1.png

Example: A group of 20 members having average age of 25 years has a new member aged 25 years. What is new average of the group?

Sol: New average of group =Description: D:\Site Articles\Average\with example\final\images\average-shortcut-methods-3-1.pngPrevious average = 25 years Number of persons excluding new member

= 20 Age of new member = 25 years Number of persons including new member = 21

Description: D:\Site Articles\Average\with example\final\images\average-shortcut-methods-3-2_cr.png

New Average when a person leaves the group

Rule 1:

In case of increase in average

Age of leaving member = Previous average – ( Increase in average × Number of members excluding leaving member)

Example:
The average weight of 10 mangos in the box is 450 grams. But accidentally one mango fell away out of the box resulting in increase of the average weight by 10 grams. What is the weight of that mango?

Sol: Age of leaving member = Previous average – ( Increase in average × Number of members excluding leaving member)Previous average

= 450 grams Increase in average = 10 grams Number of members excluding leaving member = 9 Age of leaving member = 450 – (10 × 9) = 450 – 90 = 360 grams.

Rule 2:

In case of decrease in average

Age of leaving member = Previous average + ( Decrease in average × Number of members excluding leaving member)

Example:
The average height of 10 boys is 165 cm. But one boy leaves the class and as a result there is a decrease in average height by 2 cm. What is height of leaving boy?

Sol: Age of leaving member = Previous average + ( Decrease in average × Number of members excluding leaving member)Previous average

= 165 cm Decrease in average = 2 cm Number of members excluding leaving member = 9 Age of leaving member

= 165 + ( 2 × 9) = 165 + 18 = 183 cm

Rule 3:

New average of group =

Description: D:\Site Articles\Average\with example\final\images\average-shortcut-methods-4-1.png

Example: A group of 10 persons has average age of 30 years. A person aged 40 years left the group. What is new average of the group?

Sol: New average of group =

Description: D:\Site Articles\Average\with example\final\images\average-shortcut-methods-4-1.png

Previous average = 30 years Number of persons including leaving person = 10 Age of leaving member = 40 years Number of members excluding leaving member = 9

Description: D:\Site Articles\Average\with example\final\images\average-shortcut-methods-4-2_cr.png

We hope the post is helpful. If you have any doubts please ask in comments section. Keep Studying. Stay Focused.

Happy Learning!!

– Team SSCHacks

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