AVERAGE SET 1:

1. 3 years ago, the average of a family of 5 members was 17 years. A baby having been born, the average age of the family is the same today. The present age of the baby is:
   A.5 years
   B.2 years
   C.1 year
   D.4 years
   E.None of these
   
   
   Answer – B (2 years)
   Explanation – Total age of 5 members, 3 years ago = (17 x 5) years = 85 years
   Total age of 5 members now = (85 + 3 x 5) years = 100 years
   Total age of 6 members now = (17 x 6) years = 102 years
   Age of the baby = (102 – 100) years = 2 years
   
   
   
   
   
2. Of the four numbers, the first is twice the second, the second is one-third of the third and the third is 5 times the fourth. The average of the numbers is 24.75. The largest of these numbers is:
   A.45
   B.25
   C.30
   D.45
   E.None of these
   
   
   Answer – D (45)
   Explanation – Let the fourth number be a
   then hen, third number = 5a, second number= 5a/3 and first=10a/3
   a+ 5a+ 5a/3 + 10/3 = 24.75 x 4
   so,a=9
   So, the numbers are 9, 45, 15 and 30
   
   
   
   
   
3. The average age of students of a class is 15.8 years. The average age of boys in the class is 16.4 years and that of the girls is 15.4 years. The ratio of the number of boys to the number of girls in the class is:
   A. 1 : 4
   B. 2 : 3
   C. 3 : 4
   D. 4 : 2
   E. None of these
   
   
   Answer – B (2 : 3)
   Explanation – Let the ratio be k:1
   Then, k x 16.4 + 1 x 15.4 = (k + 1) x 15.8
   (16.4 – 15.8) k = (15.8 – 15.4)
   k=2/3
   
   
   
   
   
4. The average price of 10 books is Rs. 12 while the average price of 8 of these books is Rs. 11.75. Of the remaining two books, if the price of one book is 60% more than the price of the other, what is the price of each of these two books?
   A.Rs 10 and Rs 16
   B.Rs 12 and Rs 24
   C.Rs 24 and Rs 18
   D.Rs 28 and Rs 12
   E.None of these
   
   
   Answer – A (Rs 10 and Rs 16)
   Explanation – Total price of the two books = Rs. [(12 x 10) – (11.75 x 8)]
   = Rs. (120 – 94) = Rs. 26
   Let the price of one book be Rs.x
   Then, the price of other book = Rs. (x + 60% of x )= x + (3/5)x= (8/5)x
   so, x +(8/5)x=26 , x=10
   The prices of the two books are Rs. 10 and Rs. 16
   
   
   
   
   
5. The average age of 30 boys of a class is equal to 14 years. When the age of the class teacher is included the average becomes 15 years. Find the age of the class teacher?
   A.50
   B.44
   C.45
   D.42
   E.None of these
   
   
   Answer – C (45)
   Explanation – Total ages of 30 boys = 14 x 30 = 420 years
   Total age when class teacher is included = 15 x 31 = 465 years
   Age of class teacher = 465 – 420 = 45 years
   
   
   
   
   
6. The Average of marks obtained by 120 candidates in a certain examination is 35. If the average marks of passed candidates is 39 and that of failed candidates is 15, what is the number of candidates who passed the examination?
   A.90
   B.100
   C.108
   D.115
   E.None of these
   
   
   Answer – B (100)
   Explanation – Let the number of passed candidates be a
   Then total marks =>120 x 35 = 39 a + (120 – a) x 15
   4200 = 39 a + 1800 – 15 a
   a = 100
   
   
   
   
   
7. The average of 11 results is 50. If the average of first 6 results is 49 and that of last 6is 52, find the sixth result?
   A.55
   B.56
   C.65
   D.62
   E.None of these
   
   
   Answer – B (56)
   Explanation – The total of 11 results = 11 x 50 = 550
   The total of first 6 results = 6 x 49 = 294
   The total of last 6 results = 6 x 52 = 312
   The sixth result is common to both:
   Sixth result = 294 + 312 – 550 = 56
   
   
   
   
   
8. The average age of a family of 6 members is 22 years. If the age of the youngest member be 7 years, then what was the average age of the family at the birth of the youngest member?
   A.15
   B.18
   C.28
   D.24
   E.None of these
   
   
   Answer – B (18)
   Explanation – Total age of all members = 6 x 22 = 132 years
   7 years ago, total sum of ages = 132 – (6 x 7) = 90 years
   But at that time there were 5 members in the family
   Average at that time = 90 /5 = 18 years
   
   
   
   
   
9. A batsman in his 17th innings makes a score of 85, and thereby increases his average by 3. What is his average after 17 innings?
   A.30
   B.37
   C.40
   D.45
   E.None of these
   
   
   Answer – B (37)
   Explanation – Let the average after 16th innings be a, then total score after 17th innings =>
   16a+85 = 17 (a+3)
   a = 85-51 = 34
   Average after 17 innings = a + 3 = 34 + 3 = 37
   
   
   
   
10. There were 35 students in a hostel. If the number of students increase by 7, the expenses of the mess increase by Rs 42 per day while the average expenditure per head diminishes by Rs 1. Find the original expenditure of the mess?
    A.450
    B.420
    C.430
    D.410
    E.None of these
    
    
    Answer – B (420)
    Explanation – Suppose the average expenditure was Rs a.
    Then total expenditure = 35a
    When 7 more students join the mess, total expenditure = 35a + 42
    Now, the average expenditure= (35a+42) / (35 + 7)
    Now, we have (35a + 42)/ 42 =(a – 1)
    or, 35a + 42 = 42a – 42
    7a = 84
    a = 12