Problem on AVERAGE- Quant Aptitude

PROBEM ON AVERAGE

1.  What is the average of first 21 multiples of 7 ?

1. 49
2. 147
3. 77
4. Cant be determined
5. None of these

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Explanation:

Required average  = 7(1+2+....+21) / 21
             
 =  (7/21)X ( (21x22) / 2 )  ( because sum of first 21 natural numbers [(1+2+....+21)] )
 
=  77

2.  In a class, the average age of 30 boys is 13 years and the average of 20 girls is 12 years. what is the average age of the whole class?

1. 12.5 Yrs
2. 14.2 Yrs
3. 12.3 Yrs
4. 12.6 Yrs
5. None of these

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Explanation:

Sum of age of 50 students (boys + girls)

=>  (30X 13+20 X 12) = 630
      
Average =  630/50 = 12.6 Years

3.  The average of seven numbers is 18. The average of first three numbers is 14 and the average of last three numbers is 19. What is the middle number?

1. 42
2. 57
3. 27
4. Cant be determined
5. None of these

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Explanation:

The total of seven numbers = 7X18 = 126
       
The total of first 3 and last 3 numbers is = 3 X 14+3 X 19 = 99
       
 So, the middle number is (126 - 99 ) = 27

4.  The average age of a class of 32 students is 16 yrs. if the teacher's age is also included, the average increases by one year. Find the age of the teacher

1. 49
2. 46
3. 48
4. Cant say
5. NOne of these

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Explanation:

Total age of students is 32X16 = 512 Years

 Total age inclusive of teacher = 33X (16+1) = 561

 So, Teacher's age is 561-512 = 49 Yrs
          
Shortcut trick: Teacher's age is 16+(33X1) = 49 Years :)

5.  The average weight of a class of 20 boys was calculated to be 58.4 kgs and it was later found that one weight was misread as 56 kg instead of 65 kg. What is the correct weight?

1. 67.4kg
2. 58.85kg
3. 57.75kg
4. 49.4kg
5. None of these

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Explanation:

Actual total weight is (20X 58.4 - 56 + 65) = 1177 Kgs
          
Actual average weight is 1177/20 = 58.85kgs

6.  The average weight of 8 persons increases by 1.5kg when a person weighting 65kg is replaced by a new person. What could be the weight of the new person?

1. 53kg
2. 58.85kg
3. 75kg
4. 77kg
5. None of these

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Explanation:

Let the average weight of 8 persons be 'x'

 years and the age of the new person be 'y'   years
                         
(8x - 65 + y) / 8  = x+1.5
                          
 y = 77kgs                   

Shortcut tricks: 65 + 8X1.5 = 77kgs

7.  The average temperature for Monday, Tuesday and Wednsday is 36.3 degrees C. The average temperature for Tuesday, Wednesday and Thursday is 36.7 degrees C. if Monday's temperature recorded as 39 degrees c, find the Thursday's temperature ?

1. 40.2 degrees C
2. 39.2 degrees C
3. 41.4 degrees C
4. 40.4 degrees C
5. None of these

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Explanation:

MOn + Tue + wed Temperature  =  3X36.3 = 108.9
        
Tue + wed Temperature = 108.9 - 39 = 69.9
         
Tue + wed + Thu temperature = 3X36.7 = 110.1
           
So, Thursday's temperature = 110.1 - 69.9 = 40.2 degrees C

8.  A man spends Rs. 1600 per month on an average for the first three months, Rs 1550 for next four months and Rs. 1800 per month for the last five months and saves Rs . 5200 a year. What is his average monthly income?

1. Rs. 2050
2. Rs. 210
3. Rs. 1950
4. Rs. 2200
5. None of these

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Explanation:

Total expenditure for the first 3 months = 3X1600 = 4800

Total expenditure for 4 months = 4X1550 = 6200
           
Total expenditure for 5 months = 5X1800 = 9000
           
Total expenditure and saving (which is income for one year)
               
= 4800 + 6200 + 9000 + 5200 = Rs. 25200
              
So, Average monthly income = 25200/12  =  Rs. 2100

9.  There were 45 students in a hostel, if the numbers of students increased by 7, the expenses of the mess were increased by Rs. 39 per day while the average expenditure per head diminished by Re.1. What is the original expenditure of the mess?

1. Rs. 624
2. Rs. 562
3. Rs. 585
4. Rs. 598
5. None of these

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Explanation:

Let the original expenditure be Rs.x

Original average expenditure = X/45
            
New average expenditure = (x+39)/52
   
So (x/45) - ((x+39) / 52) = 1  so x = 585
               
so, original expenditure is Rs 585

10.  The average age of father and his two sons is 27 Years. Five years ago, the average age of the two sons was 12 Years. If the difference between the ages of the two sons is four years, what is the present age of the father?

1. 42
2. 48
3. 44
4. 47
5. None of these

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Explanation:

The total present age of father and two sons is 3S27 = 81 yrs

The total present age of sons is (12+5) X 2 = 34Years

present age of father is 81 - 34 = 47 yrs

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