**SSC CHSL Topic Wise Study Material – Quantitative Aptitude – Average**

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An average or an arithmetic mean of given data is obtained when the sum of the given observations divided by number of observations.

**e.g.,** If we have to find out the average of 10,15, 25 and 30, then the required average

10+15 + 25 + 30/4 =80/4=20

Similarly, average of 30, 10 and 50 =30+10+50/3 =90/3= 30

Therefore, we can write the formula

Average (A) = Sum of given observations(S)/Number of Observations(N)=>A=S/N

**Properties of Average**

• Average of a given data is less than the greatest observation and greater than the smallest observation of the given data.

**e.g.,** Average of 3, 7, 9 and 13= 3 + 7+9+13/4=32/4=8

Clearly, 8 is less than 13 and greater than 3.

• If the observations of given data are equal, then the average will also be the same as observations.

**e.g.,** Average of 6, 6, 6 and 6 will be 6 because 6 + 6 + 6 + 6 /4=24/4=6

• If 0 (zero) is one of the observations of a given data then that 0 (zero) will also be included while calculating average.

**e.g.,** Average of 3, 6 and 0 is 3 because 3+6+0/3= 9/3 = 3

**Some Useful Facts/Formulae**

• Average of two or more groups taken together

(a) If the number of quantities in two groups be n1 and n2 and their average is x and y,respectively,the combined average (average of all of them put together) is n1x+n2y/n1+n2

(b) If the aver age of n1 quantities is x and the average of n2 quantities out of them is y, the average of remaining group (rest of the quantities) is n1x-n2y/n1-n2

**Example** The average of x numbers is y and average of y numbers is x. Then, the average of all the numbers taken together is

**SSC (10 + 2) 2012**

- (a)The average of n quantities is equal to x. When a quantity is removed, the average becomes y.

The value of the removed quantity is n (x – y) + y.

(b)The average of n quantities is equal to y. When a quantity is added, the average becomes y. The value of the new quantity is n(y – x) + y. - (a)The average of first n natural numbers is n+1/2

(b)The average of square of natural numbers till n is (n + 1)(2n + 1)/6

(c) The average of cubes of natural numbers till n is n(n+1)²/4

(d) The average of odd numbers from 1 to n is

last odd number + 1/2

(e) The average of even numbers from 1 to n is

last even number + 2/2

**Some Cases of Average Speed**

**Case I**

**Reference Corner**

**1.The average weight of Sopan, Guruprasad and Rima is 65 kg. If the average weight of Sopan and Guruprasad be 67 kg and that of Guruprasad and Rima be 57 kg, then the weight of Guruprasad is SSC (10 + 2) 2017**

(a) 60 kg

(b) 53 kg

(c) 58 kg

(d) 63 kg

**Answer:**

**2.A shop of electronic goods is closed on Monday. The average sales per day for remaining six days of a week is Rs 15640 and the average sale of Tuesday to Saturday is Rs 14124. The sales on Sunday is SSC (10 + 2) 2015**

(a) Rs 20188

(b) Data inadequate

(c) Rs 23220

(d) Rs 21704

**Answer:**

**3.The average salary of all the workers in a workshop is Rs 8000. The average salary of 7 technicians is Rs 12000 and the average salary of the rest is Rs 6000. The total number of workers in the workshop is SSC (10+2) 2014**

(a) 20

(b) 21

(c) 22

(d) 23

**Answer:**

**4.The average of two numbers is 8 and that of another three numbers is 3. The average of those five numbers is SSC (10+2) 2014**

(a) 6

(b) 5

(c) 7

(d) 5.5

**Answer:**

**5.If the average of m numbers is n² and that of n numbers is m², then the average of(m + n) numbers is SSC (10 + 2) 2013**

(a) m/n

(b) mn

(c) m – n

(d) m + n

**Answer:**

**Practice Exercise**

**1.The average of the first three numbers is double of the fourth number. If the average of all the four numbers is 12, find the 4th number**

(a) 16

(b) 48/7

(c) 20

(d) 18

**2.The average weight of 60 students in a class was calculated to be 40 kg. Later it was found out that the weight of one of the students was calculated as 36 kg, whereas his actual weight was 33 kg. What is the actual average weight of the students in the class? **

(a) 39.90 kg

(b) 39.95 kg

(c) 39 kg

(d) 38 kg

**3.A shopkeeper has a sale of Rs 6435, Rs 6927, Rs 6855, Rs 7230 and Rs 6562 for 5 consecutive months. How much sale must he have in the sixth month, so that he get an average sale of Rs 6500?**

(a)Rs 4991

(b)Rs 5991

(c)Rs 6991

(d)Rs 6001

**4.A class is divided into two sections A and B. Passing average of 20 students of section A is 80% and passing average of 30 students of section B is 70%. What is the passing average of both the sections?**

(a) 72%

(b) 74%

(c) 75%

(d) 77%

**5.Swapnil took 4 tests during first year. His average on them was 76. He took 3 tests during the second year. His average on them was 81. What was his overall average for both years?**

(a) 542/7

(b) 539/7

(c) 536/7

(d) 547/7

**6.Anand has double the money of Bharat and Bharat has 50% more money than Chetan. If average money of all the three persons is Rs 12000, how much money does Anand have?**

(a)Rs 211000/11

(b)Rs 315000/11

(c)Rs 216000/11

(d)Rs 316000/11

**7.5 yr ago, the average age of Rashi and Saurabh was 20 yr. Now, the average age of Rashi, Saurabh and Misha is 30 yr. What will be the age of Misha after 15 yr?**

(a) 35 yr

(b) 55 yr

(c) 59 yr

(d) 67 yr

**8.A cyclist rides 24 km at 16 km/h and a further 36 km at 15 km/h. Find his average speed for the journey.**

(a) 15.38 km/h

(b) 16 km/h

(c) 15.5 km/h

(d) 16.38 km/h

**9.The average salary of all the worker of the workshop is Rs 8000. The average salary of 7 technicians is Rs 6000. The total number of workers in the workshop is **

(a) 20

(b) 21

(c) 23

(d) 22

**10.A company produces an average of 4000 items per -month for the first 3 months. How much items, it must produce on an average per month over the next 9 months to average 4375 item per month over the whole year?**

(a) 4500

(b) 4600

(c) 4680

(d) 4710

**11. A certain factor employed 600 men and 400 women and the average wage was Rs 2.55 per day. If a woman got 50 paise less than a man, what were their daily wages?**

(a) Men Rs 2.75, Women Rs 2.25

(b) Men Rs 3.25, Women Rs 2.75

(c) Men Rs 3, Women Rs 2.50

(d) Men Rs 2.50, Women Rs 2

**12. The average runs scored by a cricketer in 42 innings, is 30. The difference between his maximum and minimum scores in an inning is 100. If these two innings are not taken into consideration, then the average score of remaining 40 innings is 28. Calculate the maximum runs scored by him in an innings?**

(a) 125

(b) 120

(c) 110

(d) 100

**13. A cricketer whose bowling average is 12.4 runs per wicket, takes 5 wickets for 26 runs and thereby decreases his average by 0.4. Find out the number of wickets taken by him till the last match.**

(a) 75

(b) 81

(c) 85

(d) 79

**14. The average of runs of a cricket player of 10 inning was 32. How many runs must be scored in the next inning so as to increase his average of runs by 4?**

(a) 76

(b) 70

(c) 4

(d) 2

**15. A tabulator while calculating the average marks of 100 students of an examination, by mistake enters 68, instead of 86 and obtained the average as 58; the actual average marks of those students is SSC (10 + 2) 2012**

(a) 58.18

(b) 57.82

(c) 58.81

(d) 57.28

**16. Ram aims to score an average of 80 marks in quarterly and half yearly exams. But his average in quarterly is 3 marks less than his target and that in half yearly is 2 marks more than his aim. The difference between the total marks scored in both the exams is 25. Total marks aimed by Ram is SSC (10 + 2) 2012**

(a) 380

(b) 400

(c) 410

(d) 42

**17. A library has an average number of 510 visitors on Sunday and 240 on other days. The average number of visitors per day in a month of 30 days beginning with Sunday is SSC (10 + 2) 2012**

(a) 290

(b) 285

(c) 295

(d) 300

**18. In a family, the average age of a father and a mother is 35 yr. The average age of the father, mother and their only son is 27 yr. What is the age of the son? SSC (10 + 2) 2012**

(a)12yr

(b)11yr

(c)10.5yr

(d)10yr

**Answers**

**Hints & Solutions**

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