Quantitative Techniques: Averages: CLAT 2020

Just Imagine your father coming home from the office and bringing 12 chocolates for you and your 3 cousins (A, B, C). You got 2 chocolates, A got 4, B got 5 and C got 1.

You and C starts fighting about how A and B got more chocolates. In your head, you calculated that everyone should have got 3 chocolates but that didn’t happen. The number 3 that you calculated is technically called an Average.

In simple terms, an average is distributing x number of items equally in n number of groups. Here x is the sum of observations(Observations in the above description are chocolates each individual got) and n is the number of observations(No. of individuals).

Important Notes: Averages questions can come in exam clubbed with other topics like height/weight/age/speed, time and distance/Arithmetic Progression

When a Person replaces another person in the group(age, weight, height and similar kind of Problems)

When someone joins the group

Note: With the new format of Clat one cannot expect direct questions from any topic. Implementation of whatever you learnt simultaneously is important to solve Quantitative Techniques Averages for CLAT.

= 38*24 = 912 kg

New average = 38+2 = 39.5 kg

Total number of People = 24+1 (including teacher) = 25

New total of weights= 39.5*25 = 987.5

Weight of teacher= New total of weights – Previous Total weights of Students

= 987.5-912 = 75.5 kg

Shortcut: As the question says there is an increase in the average by 1.5 kg when teacher’s weight is also considered so we will apply the formula discussed above

Teachers age= Earlier Average+(Increase in average*Total number of people)

                      =  38 + (1.5*25)

=  38 + (37.5) = 75.5 kg

*See the difference in conventional and shortcut method, Due to involvement of numerous steps the conventional method becomes more time taking although it’s not too long if you are in a habit of oral number crunching but if not then it is advised to use shortcuts.*

Solution: Let the speed of Train be x and speed of bus be y. By applying the Average Speed formula we get,

Average Speed = (2*x*y)/x+y

= 2*92*54 / (92+54)

= 9936/146 = 68.05 km

Solution: If the number of days in a month is 30 then there would be 4 complete weeks + 2 days. 4 weeks means 4 Sundays with 580 customers thus 26 normal days with 250 customers.

Total Number of Customers = Customers on Sunday + Customers on other days

= 580*4 + 250*26 = 2320 + 6500

= 8820

Number of Daya = 30

Average Number of Customers in a day=Total number of customers/Number of Days  = 8820/30 = 294 customers/day 

Solution:  As we need average of Viraj’s last 7 matches run we will first find out how many runs he made in those last 7 matches by subtracting runs of his first 8 matches from total runs.

Total Runs made by Viraj in 15 matches=Average runs made*No. of matches = 42.8*15

             = 642

Runs made by viraj in first 8 marches = 55.4*8

= 443.2

Runs made by Viraj in last 7 matches = 642-443.2

= 198.8

The average number of runs made by Viraj in his last 7 matches = 198.8/7

=28.4

Solution: Here you are provided with a series and the first thing you will do is start adding to find the average, but the trick in the question is you don’t need to follow usual steps. Here apply you some logical reasoning observe that the series holds a pattern where each successive term is found by adding 3 to it. Thus making it an AP with a difference of 3.

And when you figure that you have an AP with 5 terms(odd) in the question you can directly answer without picking your pen that the middle term is your answer, i.e, 8 would be the Average of this series.

Coming to the second part of the question you are required to add a term in the series with a difference of 3 at the end and it is a successive term. Making the number of terms in the series even (2, 5, 8, 11, 14, 17) we would use the second shortcut which says find the average of middle 2 terms ((8+11)/2) i.e, 9.5.

The average age of A, B, C, D is 32 years. Find the age of D.

Statement I: the sum of ages to A and B is 54 years

Statement II: C is 10 years older than D

   Solution: Age of A and B = A+B = 54 years                     …eqn (i)

Sum of ages of A, B, C, D = A+B+C+D = 32*4            …eqn(ii)

Age of D = Age of C + 10 years => D=C+10                …eqn(iii)

Using the above 3 equations that came from statements I and II, we can answer the question but none of the statements alone is sufficient to answer the question. Hence the answer would be D which says both the statements are required together to answer the question.