From the examination point of view, each and every topic is important. Due to the complexity and rise in the level of the quantitative aptitude section, it is necessary to have deep knowledge about the important topics to be covered for the IBPS PO exam 2019. For that, we have already provided you with the detailed

**IBPS PO Study plan**named Kar IBPS Fateh. Do not miss to practice from the different number of questions to ace your speed in the exam. You can also refer to the**daily quizzes**on different topics provided on bankersadda. Do not miss out to the tips and tricks to solve the Average and age problems. continue reading this post to know how can you ace the aforementioned topic.###
**Average**

→ An average of a given data is the sum of the given observations divided by the number of observations

→ For ex, average of 24, 32, 40, 48

*** Some important rules of average are as follow:-**

→ Average of a given data is less than the greatest number and greater than the smallest number

→ If 0 (zero) is one of the numbers of a given data, then that 0 (zero) will also be included while calculating average

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**Important formulas of average:-**

→

**Different types of questions which are asked in the exams nowadays are as follow:-**
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**Type 1:-**

If the average of m1 numbers is x1 and the average of m2 numbers is x2 and so on, then

*** Type 2:-**

If the average of x observations is C and average of y observation taken out from x is d, then

average of rest of the numbers

*** Type 3:-**

If the average of

**x**students in a class is**M**, while average of passed student is**a**and average of failed student is**b**, then**Ex)**In a class, there are 50 students and average marks in the exam is 40. If average marks of passed student is 50 and average marks of failed student is 25, find number of students who failed?

→ Let, no. of students failed = x

Then, no. of students who passed = 50 – x

∴ 50 × 40 = 25x + 50 (50 – x)

∴ 2000 = 25x + 2500 – 50x

∴ –500 = –25x

∴ 25x = 500

x = 20

∴ Failed student = 20

*** Type 4:-**

Average speed is defined as total distance travelled divided by total time taken

**Ex)**A man covers a certain distance by bike at 25 km/hr and comes back at a speed of 50 km/hr. What is his average speed during travel?

→ Here A = 25 km/hr, B = 50 km/hr

**→ Some other examples related to the given formula as given above:-**

**Ex)**Find average of numbers from I to 31

∴ average

Here n = 31

**Ex)**Find out the average of 2, 4, 6, 8, 10, 12, 14, 16, 18 and 20

→ Here, n = 10

∴ Required average = (n + 1)

= (10 + 1)

= 11

**Ex)**Find out the average of 3, 6, 9, 12, 15, …….. , 30, 33

∴ Here, 1st number = 3

Last number = 33

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**Problem based on Ages:-**

**→ Age is defined as the period of time that a person has lived. Age is measured in month, year**

→ Problem based on ages generally consists of information of ages of two or more person and a relation between their ages in present /future/past

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**Different types of Questions or technique used in problem based on Ages***** Type 1-**If ratio of present ages of A and B is c : d and x yr ago, their ages was m : n, then

**Ex)**If present age of Amar is 3 times the age of Suresh and if 8 years ago, then Amar age ratio will be 7 times the age of Suresh , then find present age of Amar?

Let amar’s age be 3x and Suresh’s age be x

∴ 3x – 8 = 7x – 56

∴ 4x = 48

∴ x = 12

∴ Present age of Suresh = 3x

= 3 × 12 = 36 yrs.

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**Type 2:-**If ratio of present age of P and Q is a : b and after n years, the ratio of their ages will be c : d, then**Ex)**If ratio of present age of Sonal and Keerti is 3 : 5, and if after 12 years, their ages will be in the ratio 9 : 13, then find present age of Keerti?

→ Let Sonal’s present age be 3x and Keerti’s present age be 5x

∴ 39x + 156 = 45x + 108

∴ 6x = 48

∴ x = 8

∴ Keerti’s present age = 5x = 40 yrs.

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**Type 3 :-**If X is as much older than Y as he is younger to Z and sum of ages of Y and Z is b yrs. then their age order is Y < X < Z
i.e. Here Z is the oldest and Y is the youngest

**Ex)**If Ashish is as much elder than Saurav as he is younger to Jayant and Sum of ages of Saurav and Jayant is 42 yrs, then find Ashish’s age?

Let Ashish’s present age is x yr and he is y Rs younger to Jayant

∴ Jayant’s age = (x + y) yrs

Saurav’s age = (x – y) yrs

∴ Sum of ages of Jayant and Saurav

⇒ (x + y) + (x – y) = 42

⇒ 2x = 42

⇒ x = 21

∴ Ashish present age = 21 yr

*** Faster approach:-**

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**Type 4:-**If b yrs after age of one person is x times of that of another person and at present the age of first person is y times of that of another person, then**Ex)**Present age of Gautam is 5 times the age of Shivani and after 10 years, Gautam will be 3 times as sold as Shivani, find present ages of Gautam and Shivani?

Let Present age of Gautam = 5x yr

∴ Present age of Shivani = x yr

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