** Average practice set 1**

**Example 1:** The average of four consecutive even numbers A, B, C and D respectively is 35. What is the product of A & C ?

**Solution :** let the first A = x

35 = x+x+2+x+4+x+6/4

A = 32

Product = 32 x 36 = 1152

**Example 2:** Average score of Rohan, Monty and Sujay is 64. Rohan’s Score is 16 less than Anil and 12 more than Monty. If Anil Scored 25 marks more than the average score of Rohan, Monty and Sujay, What is the sum of Monty and Sujay scores ?

**Answer:**

Rohan + Monty + Sujay = 192

Anil = 89

Rohan = 73

Monty = 61

Sujay = 58

Sujay + Monty = 58 + 61 = 119

**Example 3:** The average height of four girls was recorded as 160cms. If the average of the heights of three girls out of the four was 162cms. What was the height of the fourth girl?

**Solution :** 160×4 – 162×3

= 640 – 486

=154 cms.

**Example 4:**

In a School of 8 student average weight is increased by 3.5 kg, when new student comes in place of one of them than weight become 55 kg, what would be the weight of the new student ?

**Answer :**

Step 1: At first we find the total weight increased So, ( 8 X 3.5 )kg = 28 kg.

Step 2: Now the weight of new Student is = ( 55 + 28 )kg = 83 kg.

So, the weight of the new student is 83 kg.

**Example 5:**

In an examination it is required to get 34% of the aggregate marks to pass. A student gets 270 marks and is declared failed by 7% marks. What are the maximum aggregate marks a student can get ?

**Answer :**

Step 1: 34% = 270 + 7%

Step 2: 27% = 270

Step 3: 100% = 270 x 100 / 27 = 1000 marks.

**Example 6:**

Rajan obtain 56, 75, 78, 86 and 88 marks out of 100 in Physics, Life Science, Mathematics, Biology, and Computer. What are her average marks ?

**Answer :**

Step 1: Average of all subject marks 56 + 75 + 78 + 86 + 88 / 5

=383 / 5 = 76.6.

**Example 7:**

Find the average of all the numbers between 6 and 34 which are divisible by 5.

**Answer:**

Step 1: 10 + 15 + 20 + 25 + 30 which are divisible by 5 in between 6 and 34

So average of number is 10 + 15 + 20 + 25 + 30 / 5 = 100 / 5 = 20.

**Example 8:**

There are two section X and Y of a College, consisting of 36 and 44 students respectively. if the average weight of section X is 40 Kg and that of section Y is 35 Kg. Find the average weight of the whole College (in Kg) ?

**Answer:**

Step 1: At first the total ( X + Y ) college students are ( 36 + 44 ) = 80.

Step 2: college X total student weight and college Y total student weight is ( 36 x 40 + 44 x 35 ) = 2980

Average weight of the whole college is = 2980 / 80 = 37.25.

**Example 9:** The average of Six numbers is 49. If the average of first five numbers is 59, What is the value of the sixth number ?

**Anawer :**

Sum of six numbers = 62 x 6 = 372

Sum of first five number = 59 x 5 = 295

So, the 6th number is ( 372 – 295 ) = 77.

**Example 10:**

Find the average of the following set of scores ?

357 , 854 , 214 , 648 , 478

**Answer :**

2551 / 5

= 510.2

So the average of five numbers is 510.2.

**Example 11:**

The average age of 15 boys is 18 years in the Maths class and that of 13 girls is ages 15 years.What is the average age of total maths class ?

**Answer :**

In a maths class 15 boys ages 18 years = ( 15 x 18 ) = 270

In a maths class 13 girls ages 15 years = ( 13 x 15 ) = 195

So average age of total maths class is = 270 + 195 / 28 = 465 / 28 = 16.607.

**Example 12:**

The average of 5 numbers is 4.5. If average of two number is 3.5 and that of another two numbers is 3.7, then what is the last number?

**Answer :**

2 x 3.5 = 7

2 x 3.7 = 7.4

5 x 4.5 = 22.5

( 22.5 – 7.4 + 7 ) = 8.1

So the last number is 8.1.

**Example 13:**

The average of Five numbers is 62. The average of the second and the third number is 45. The average of the first and the fifth number is 66. What would be the fourth number ?

**Answer :**

Average of Five numbers is = 62 x 5 = 310

Average of second and third number = 45 x 2 = 90

Average of first and fourth number = 66 x 2 = 132

( 132 + 90 ) = 222

The fourth number is ( 310 – 222 ) = 88.

**Example 14:** If the average of 8 numbers is 2.85. If the two number average is 2.3 and other two number average is 3.9, then Find the average of other two numbers ?

**Answer:**

22.8 – ( 4.6 + 7.8 ) / 2

= 22.8 – 12.4 / 2 = 5.2

the average of other two numbers 5.2.

**Example 15:** The average of 5 consecutive even number P, Q, R, S and T is 42. What is the product of P and R ?

**Answer :**

P Q R S T

38 40 42 44 46

38 X 42 = 1596.

**Example 16:**

In a school of class x after replacing an old student by new student, it was found that the average age of eight student of a class x is the same as it was 5 years ago. What is the differences between the ages of the replaced and new student ?

**Answer :** Age decreased = ( 8 x 5 ) = 40 years.

So the required age difference is = 40 years.

**Example 17:**

The average monthly income of A and B is Rs.6040. The monthly average income of B and C is Rs.7500 and monthly average income of A and C is Rs. 6500. Find the income of A in a monthly income ?

**Answer:**

Step 1: here is ABC given respectively monthly income, hence we need to find both income.

( A + B ) = ( 6040 x 2 ) = 12080, ( B + C ) =( 7500 x 2 ) = 15000, ( C + A ) = ( 6500 x 2 ) = 13000

Step 2: If we add 3 income 2( A + B + C ) = 2 x ( 12080 + 15000 + 13000 ) = 40080 or A + B + C = 40080 / 2 = 20040.

Step 3: So we get the income of A Subtract income of ( A + B + C ) – ( B + C ) = (20040 – 15000 ) = 5040.5.

**Example 18:**

The average of 4 consecutive odd numbers P , Q , R , S is 66. What would be the product of P and S?

**Answer :**

Average is 66

P Q R S

63 64 65 66 67 68 69

Product of ( P x S ) = ( 63 x 69 ) = 4347.

**Example 19:** In a office the average salary of employee is Rs.7000. The average salary of 6 office employee is Rs. 12,000 and the rest of employee salary is Rs.5000. Find the total number of employee in that office.

**Answer:** let the total number of employee is x, and average of all employee is

= 7000 = 7000x.

average salary of 6 employee is = 12,000 = 6 x 12,000 = 72,000.

So remaining average of employee is = 5000 X ( x – 6 ) = 5000x – 30,000

7000x = 72,000 + 5000x – 30,000

2000x = 42,000

x = 21.

**Example 20:**

A city center has an average of 610 visitors on Sunday and 340 on other days. The average number of visitors per day in a month of 30 days Beginning with a Sunday is.

**Answer :**

Since the month begins with a Sunday, So there will be five Sundays in the month

= ( 610 x 5 + 340 x 25 ) / 30

= 3050 + 8500 / 30

=11550 / 30 = 385.

**Example 21:**

The average marks of first 54 group members is 62 and second 62 group members is 65, and third 48 group members is 70 respectively then, What would be the average marks of all the students ?

**Answer :**

Step 1: At First we find the total students marks according with 3 group

= ( 54 x 62 ) + ( 62 x 65 ) + ( 48 x 70 ) = ( 3348 + 4030 + 3360 ) = 10738.

Step 2: Now we need to find average marks of all three groups is,

Total groups members are = ( 54 + 62 + 48 ) = 164.

the average marks of all the students = 10738 / 164 = 65.47.

**Example 22:**

The average marks in english subject of a class of 24 students is 56.If the marks of the students were misread as 44,45 and 60 of the actual marks 48, 59 and 66 respectively, then what would be the correct average ?

**Answer:** **Average :** 24×56(173-149)/24 = 57

**Example 23:** Ranjan’s monthly income is three-fifth rina’s monthly income. Rina’s monthly income is Rs.36,000/-. What is average monthly income of Ranjan and Rina together ?

**Answer:** 36,000×3/5 = 21,600

36,000+21,600/2 = 28,800.

**Example 24:** The marks of six girls in a group are 149,158,189,137,178 and 161. What are the average marks of all six boys ?

**Answer:** average number = 149 + 158 + 189 + 137 + 178 + 161/6 = 972/6 = 162.

**Example 25:** A car covers the first 39kms. of its journey in 40 minutes and covers the remaining 26kms. in 35 minutes, What is the average speed of the car ?

**Answer:** 39+26 x 60/75 = 52km/hr

**Example 26:** The average speed of a bike is 9/4 times the average speed of a car. A tractor covers 598 km in 23 hours. how much distance will the bike cover in 4 hours if the speed of the car is twice speed of the tractor ?

**Answer :** speed of bike = 9 x speed of car /4

speed of tractor = 598 /23 = 26km/hr.

speed of car=52km/hr.

speed of bike = 52 x9/4 = 117

car covers distance in 1 hour.

4 hours covers = 117 x 4 = 468km.

**Example 27:**

The average age of 15 boys is 18 years in the Maths class and that of 13 girls is ages 15 years. What is the average age of total maths class ?

**Answer :**

In a maths class 15 boys ages 18 years = ( 15 x 18 ) = 270

In a maths class 13 girls ages 15 years = ( 13 x 15 ) = 195

So average age of total maths class is = 270 + 195 / 28 = 465 / 28 = 16.607.

**Example 28:** If the average of 8 numbers is 2.85. If the two number average is 2.3 and other two number average is 3.9, then Find the average of other two numbers ?

**Answer:**

22.8 – ( 4.6 + 7.8 ) / 2

= 22.8 – 12.4 / 2 = 5.2

the average of other two numbers 5.2.

**Example 29:** The average speed of a bike is 9/4 times the average speed of a car. A bus covers 540km in 27 hours. How much distance will the bike cover in 5 hours, if the speed of the car is twice speed of the bus?

**Solution :**

Speed of bike = 9xspeed of car/4

speed of bus = 540/27 = 20km/hr

speed of car = 40km/hr

speed of bike = 40 x 9/4 = 90km/hr

distance covers by bike in 1hr = 90km

5 hrs = 90×5 = 450km.

**Example 30:** In annual exam puja scored 54 percent marks, ramala scored 68 percent marks and Rubi scored 76 percent of marks.

The maximum marks of the exam are 750. What are the average marks scored by all the three girls together?

**Answer :** 405 + 510 + 570 / 3 = 495

**Example 31:**

The average of five number is 56. if the average number of first four numbers is 54, What is the value of the fifth number.

**Answer :** Average of five number is 57*5=285

Average of first four numbers is 54*4=216

The value of the fifth number = (285 – 216) = 69

Example 32:

In an school exam Ritesh scored 52% marks, Sujay scored 64% marks and Rajiv scored 74% of marks. The maximum marks of the exam are 750.

What are the average marks scored by all the three boys together ?

Answer : 390+480+555/3 = 475