# Average

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Hello sir, Can you please explain this question

Rajiv is a student in a business school. After every test he calculates his cumulative average. QT and OB were his last two tests. 83 marks in QT increased his average by 2. 75 marks in OB further increased his average by 1. Reasoning is the next test, if he gets 51 in Reasoning, his average will be _____?

1. 63
2. 62
3. 61
4. 60

Hello Ritika,

Find the solution.........

Let initial average =a and number of subjects = n

According to first condition,

an + 83 = (n+1) (a + 2)

an + 83 = an + 2n + a + 2

a + 2n = 81…………………1)

According to second condition,

{(a + 2) (n + 1)+ 75} = (a+2+1)(n+2)

an + a +2n + 2 + 75 = an + 2a + 3n + 6

a + n =71 …………………………..2)

From eq. 1) and 2)

n = 10 and x = 61

After paper OT and OB

Average = 61 + 2 + 1 =64

Number of subjects = 10 + 1 + 1 =12

So after getting 51 in reasoning,

Average = (64 x 12 + 51)/(13) =819/13=63

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the average of m students should be more than 40 to give total average more than 40 for maximum we will take m=5 and n=45, than

total avg =(40*40+45*5)/40+5

=1825/45

=40.5555

hence option 2 is correct

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In June a football team played 60 games and won 30% of these. After a phenomenal winning streak , this team raised its average to 50% . How many games did the team win in a row to attain this average?

30% of 60 = 18 .

Let the team played n matches in a row .

so , ( 18 + n)/(60 + n ) = 1/2

n = 24  .

Hence,the team won 24 matches in a row .

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In an office, there are n employees and their average age is 36 years. After two years, 5 employees whose average age is 40 years, leave the office and next after three years 5 employees whose average age is 30 years, joined the office. Now the average age of the employees of the office becomes 39.7 years. Find the number of employees in the office initially.

after two years average will become 38 then the total age of all employees =38n

5 people of age 40 leave then total age=38n-40*5  =38n-200

after 3 more years so then total age=(38n-200) +(n-5)3            [n-5 is because five employee have already left ]

then comes 5 people of age 30 then total age become =(38n-200) +(n-5)3 +30*5

now total people are still  n and the average now is 39.7

{(38n-200) +(n-5)3 +150}/n =39.7

41n -200 +150-15 =39.7

1.3n=65

n=50

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Hi Pulkit,

let the average height of 22 toddlers be 3x .

so the average height of two toddlers who left => x

Sum of the heights of 22 toddlers = 66x

Sum of the heights of  remaining 20 toddlers = 66x - 2x = 64x

According to question ,

64x/20 - 66x/22 = 2

3.2x - 3x = 2

x = 10

hence the average height of the remaining toddlers = 3.2 x 10 = 32

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a set of consecutive positive integers beginning with 1 is written on the blackboard .a student came along and erased one number.the average of the remaining  numbers is 37(31/37).what was erased number?

The average is 37  31/37 = 1400/37

we know that average of 1st n consecutive number is (n+1)/2 but average is 35 31/37 hence
value of n should be close to 2 x 37= 74. If there are n numbers then after erasing we will have n-1 numbers then summation of the n-1 numbers = (n-1) x Avg  = 1400(n-1)/37, hence n-1 should be divisible by 37, but n is close to 74 ,  hence n = 75 so that n-1 =74 is divisible by 37. Hence n = 75.

Sum of 1st 75 natural numbers = 75 x 76/2  = 2850
Sum of 74 number after erasing one number = 1400/37 x 74 = 2800
Hence the number that was erased = 2850 - 2800 =50 .

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The average of the squares of First 'n' natural numbers starting from 1 is 130 . Then , what is the average of the cubes of these first n natural numbers ?

avg of square of first n natural nos is (n+1)(2n+1)/6=130

2n^2+3n+1=780

2n^2+3n-779=0

n=[-3+√(9+6232)]/2

n=38

sum of cube of first n natural nos. is ( n ( n +1)/2)2

put value of n

38*39*38*39/4

avg=sum/n

=(38*39*38*39)/4*38

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Swati has three cartons of books. The average price of the books in carton 1 was Rs 64, the average price of the books in Carton 2 was Rs 82 and the average price of the books in Carton 3 was Rs 95. The average price of all the books in Carton 1 and Carton 2 together was Rs 78 and the average price of all the books in Carton 2 and carton 3 together was Rs 90. What was the average price of the the books of three cartons?

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A shipping clerk has five boxes of different but unknown weights. The clerk weighs the boxes in pairs. The weights obtained are 101, 102, 103, 104, 105, 106, 107, 108, 109, 111kg. What is the weight of the heaviest box?

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Average of first n natural nos is (n+1)2=x

next n nos will be

n , n+1, n+2, n+3.......2n

their sum =n*n+ n(n+1)/2

average ={n*n+ n(n+1)/2}/n

average = n+x

hence option A

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Sir , kindly share the solution to this question -

4! ( 4C4 + 5C4 + 6C4 +...+14C4

Sum :  4! (15C5) = 72072

Average : 72072/11 = 6552

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Let the free luggage allowance be x kg.

M + S = 1050... (1)
x + 2M = 2400 ... (2)

x + 2S = 900 ... (3)

from (1) , (2) and (3)
x = 600
M = 900

98.

4! ( 4C4 + 5C4 + 6C4 +...+14C4

Sum :  4! (15C5) = 72072

Average : 72072/11 = 6552

Sir, why have you used C?

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the average age of 200 employees in an organization in 1990 was 40 yrs. in 1992, 40 employees whose avg age was 50 yrs, left the organisation. after 4 years , 20 employees whose avg age was 32 yrs, joined the organisation. what was the avg age of all the employees in the year 2000?

 Year No ofemployees sum of age of all employees Avg Age Remark 1990 200 (200*40) 1992 (200-40) = 160 (200*42)-(40*50) in 2 years avg age will increase by 2 1996 (200-40+20) = 180 (200*46)-(40*54)+(20*32) in next 4 years avg age will increase by 4 2000 (200-40+20) = 180 (200*50)-(40*58)+(20*36) = 8400 (8440/180) = 46.7 in next 4 years avg will increase by 4
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There are seven consecutive natural numbers such that the average of the first five is
n. Then the average of all seven numbers will be
A. n
B. n+1
C. kn+1/k, where k is a positive constant
D. n+2/7

Average of natural number increases by 0.5, if next natural number is added in the list

example ( avg of 3,4,5 is 4. and Avg of 3,4,5,6 is 4.5)
hence when we add two consecutive natural numbers avg will increase by 0.5+0.5 = 1

hence new avg will be n+1

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