### 23 May

It has been seen that candidates engaged in SSC, IBPS and SBI exam preparation are generally aware of the basic concepts related to Arithmetic. They can solve exam questions using the step-based methods learnt at high school level. However, when it comes to competitive exams, these methods don’t prove to be much useful because they are quite time consuming.

If you persist with such methods, then cracking Quantitative Aptitude will become a tough task. Within this section, Averages is an important topic to deal with. Therefore, the teachers from the ** institute for Best SSC CGL Coaching in Delhi **have explained below the shortcuts and tricks you must know to handle problems based on averages.

**Short Tricks & Tips**

**TYPE 1****: If a new student comes to class and because of this the average age of students increases, then what will be the age of the new student?**

**NEWCOMER’s AGE = OLD AVERAGE AGE + (PRESENT NUMBER OF STUDENTS × INCREASE IN AVERAGE)**

**OR**

**If a new boy comes to class and because of this the average age of students decreases, then what will be the age of the new boy?**

**NEWCOMER’s AGE = OLD AVERAGE AGE –**** (PRESENT NUMBER OF STUDENTS × DECREASE IN AVERAGE)**

**Question – I****: ****The average age of a class of 35 students is 14.8 years. A new student joins the class and the average becomes 14.9 years. The age of the newcomer is **(A) 18.4 (B) 16.3 (C) 17.4 (D) None of these

**Solution: (A)**

Let the age of the new student also be 14.8 years. In such a case, the average age of all 36 students (35 students + 1 new student = 36 students) remains the same, which is 14.8 years.

But, this is not the case. On arrival of the new student, the average increases by 0.1 years = (14.9 – 14.8). So, 0.1 years is added to all 36 students of the class.

It means the newcomer’s age should be more than 14.8 years. How much more? It is 0.1 × 36 = 3.6 years more. Hence, the age will be 14.8 + 3.6 = **18.4 years.**

**FORMULA METHOD**

NEWCOMER’s AGE = OLD AVERAGE AGE + (PRESENT NUMBER OF STUDENTS × INCREASE IN AVERAGE)

In the above case, Newcomer’s age = 14.8 + (0.1 × 3.6) = 14.8 + 3.6 =** 18.4 years**

**Question – II****: ****The average weight of a coaching class having 24 students is 35 kg. If the weight of the teacher is also included, the average goes up by 400 grams. The weight of the teacher in kg is **(A) 45 (B) 50 (C) 53 (D) 55

**Solution: (A)**

Average weight of a class of 24 students = 35 kg & when the teacher joins the class, the average rises by 400 gm.

TEACHER’s WEIGHT = OLD AVERAGE WEIGHT + (PRESENT NUMBER OF PEOPLE × INCREASE IN AVERAGE)

Teacher’s weight = 35 kg + (400 gm × 25) = 35 kg + 10000 gm = **35 kg + 10 kg = 45 kg**

**Question – III****: ****A cricket player has a certain average score in 10 innings. In the 11 ^{th} innings, he scored 108 runs, thereby increasing his average score by 6 runs. His new average score is: **(A) 48 (B) 52 (C) 55 (D) 60

**Solution: (A)**

Let the average runs of 10 innings = x** **& after 1 more inning, the average of 11 innings = x + 6

NEW SCORE = OLD AVERAGE + (PRESENT NUMBER OF INNINGS × INCREASE IN AVERAGE)

108 = x + ( 6× 11)

108 = x + 66 or x = 108 – 66 = 42

So, the new average = x + 6 = 42 + 6 = **48**

**Question – IV****: ****The average of 5 numbers is 140. If a number is excluded, the average of the remaining 4 numbers is 130. The excluded number is **(A) 180 (B) 170 (C) 160 (D) 190

**Solution: (A)**

Average of 5 numbers = 140**. **If a number is now excluded, then the average of remaining 4 numbers = 130. So, we will write this INVERSELY. It will then become the same case as that of a newcomer.

Average of 4 numbers = 130 & average of 5 numbers = 140

NUMBER EXCLUDED (or NOW REMOVED) = OLD AVERAGE + (PRESENT NUMBER × INCREASE IN AVERAGE)

Number excluded = 130 + (5 × 10) = 130 + 50 = **180**

**TYPE 2****: If a boy is replaced with a new boy & this affects their averages, then what will be the age of the new boy?**

**NEWCOMER’s AGE = AGE OF REMOVED BOY + (PRESENT NUMBER OF BOYS × INCREASE IN AVERAGE)**

**OR**

**NEWCOMER’s AGE = AGE OF REMOVED BOY **–** (PRESENT NUMBER OF BOYS × DECREASE IN AVERAGE)**

**Question – V****:**** The average weight of 4 men is increased by 3 kg, when one of them whose weight is 120 kg is replaced by another man. What is the weight of the new man?**

**Solution: 132 kg**

NEWCOMER’s WEIGHT = WEIGHT OF MAN REMOVED + (PRESENT NUMBER OF MEN × INCREASE IN AVERAGE)

Weight of the new man = 120 + 4 × 3 = 120 + 12 = **132 kg**

**Question-VI****:**** In a class, there are 20 boys whose average age is decreased by 2 months, when one boy of 18 years age is replaced by a new boy. Find the age of the new boy.**

**Solution: 14 years 8 months**

Age of the new boy = Age of the removed boy – No. of boys × Decrease in average age

= 18 years – 20 × 2 months = 18 years – 40 months

= 18 years – 3 years 4 months =** 14 years 8 months**

**Question-VII****:**** The average age of 8 persons in a committee is increased by 2 years when two men aged 35 years & 45 years are substituted by 2 women. Find the average age of these two women.**

**Solution: 48 years**

When two men are replaced by two women and the average increases, then the total age of two women = Total age of two men + Number of persons × increase in average

= (35 + 45) + 2 × 8 = 80 + 16 = 96 years.

Average age of two women = total age of two women / 2 = (96 / 2) = **48 years.**

**Question-VIII****:**** The average temperature on Wednesday, Thursday and Friday was 25 ^{o}. The average temperature on Thursday, Friday & Saturday was 24 degrees. If the temperature on Saturday was 27^{o}, what was the temperature on Wednesday?**

**Solution: ****30 ^{o}**

Average temperature of (Wednesday, Thursday & Friday) = 25^{ o}

Average temperature of (Thursday, Friday & Saturday) = 24^{ o}

Now, it is also a case of replacement, here Wednesday is replaced by Saturday & the average decreases.

So, the temperature on Saturday = temperature on Wednesday – number of days × decrease in average.

27** ^{o }**= temperature on Wednesday – 3 × 1

So, the temperature on Wednesday = 27 + 3** = 30 ^{o}**

With the help of solved examples presented above, you have now covered the time saving shortcuts involved in cracking average based questions. However, further practice will be required, from here, to strengthen the learning that has taken place. In this regard, the model papers and online test series offered by the ** center for Top IBPS Coaching in Delhi** will definitely be the right resource for you.

**Summary**

This article based on the topic averages will be most useful for students involved in Govt. job exam preparation. To learn further from Vidya Guru Experts and to get your doubts and queries answered, you can write to vidyagurudelhi@gmail.com.

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