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Monday, 29 April 2019

MATHS SOLVED IN STEPS: Problems on Average - 03

23. If the average marks of three batches of 55, 60 and 45 students respectively is 50, 55, 60, what is the average marks of all the students?
A. 53.23               B. 54.68              C. 51.33              D. 50
Answer : Option B
Explanation :
Average marks of batch1 = 50
Students in batch1 = 55
Total marks of batch1=55×50
Average marks of batch2 = 55
Students in batch2 = 60
Total marks of batch2=60×55
Average marks of batch3 = 60
Students in batch3 = 45
Total marks of batch3=45×60
Total students = 55 + 60 + 45 = 160
Average marks of all the students
= {(55×50)+(60×55)+(45×60)}/160
= (275+330+270)/16
= 875/16=54.68


24. A library has an average of 510 visitors on Sundays and 240 on other days. What is the average number of visitors per day in a month of 30 days beginning with a Sunday?
A. 290                   B. 304                 C. 285               D. 270
Answer : Option C
Explanation :in a month of 30 days beginning with a Sunday, there will be 4 complete weeks and another two days which will be Sunday and Monday Hence there will be 5 Sundays and 25 other days in a month of 30 days beginning with a Sunday
Average visitors on Sundays = 510
Total visitors of 5 Sundays = 510×5
Average visitors on other days = 240
Total visitors of other 25 days = 240×25
Total visitors = (510×5)+(240×25)
Total days= 30
Average number of visitors per day ={ (510×5) +  (240×25)}/30
= { (51×5)+(24×25)  }/3
=   (17×5) + (8×25)
=85+200=285

25. A student’s mark was wrongly entered as 83 instead of 63. Due to that the average marks for the class got increased by half 1/2. What is the number of students in the class?
A. 45               B. 40                  C. 35             D. 30
Answer : Option B
Explanation : Let the total number of students = x
The average marks increased by 1/2 due to anincrease of 83-63=20 marks.
But total increase in the marks = 1/2×x=x/2
Hence we can write asx/2=20•Ëx=20×2=40


26. A family consists of two grandparents, two parents and three grandchildren. The average age of the grandparents is 67 years, that of the parents is 35 years and that of the grandchildren is 6 years. The average age of the family is
A. 32.27 years       B. 31.71 years       C. 28.17 years   D. 30.57 years
Answer : Option B
Explanation :
Total age of the grandparents = 67×2
Total age of the parents = 35×2
Total age of the grandchildren = 6×3
Average age of the family ={(67×2)+(35×2)+(6×3)}/7=(134+70+18)/ 7=222/7=31.71

27. The average weight of A, B and C is 45 kg. If the average weight of A and B be 40 kg and that of B and C be 43 kg, what is the weight of B?
A. 31 kg                 B. 2812 kg             C. 32 kg                D. 3012 kg
Answer : Option A
Explanation :
Let the weight of A, B and C are a,b and c respectively.
Average weight of A,B and C = a+b+c=45×3=135—equation(1)
average weight of A and B = 40 a+b=40×2=80—equation(2)
average weight of B and C = 43 b+c=43×2=86 —equation  (3)
equation(2) +equation(3)- equation(1)
=> a+ b+ b +c “(a +b +c)=80+86”135
=>b=80+86"135=166"135=31
=> weight of B = 31


28. The average age of husband, wife and their child 3 years ago was 27 years and that of wife and the child 5 years ago was 20 years. What is the present age of the husband?
A. 40                 B. 32             C. 28            D. 30
Answer : Option A
Explanation :
let the present age of the husband = h
present age of the wife = w
present age of the child = c
3 years ago, average age of husband, wife andtheir child = 27
= >Sum of age of husband, wife and their child before 3 years = 3×27=81
= > (h-3) + (w-3) + (c-3) = 81
= > h + w + c = 81+9 = 90 ————————— equation(1)
5 years ago, average age of wife and child = 20
= >Sum of age of wife and child before 5 years = 2×20=40
= > (w-5) + (c-5) = 40
= > w + c = 40+10 = 50 —————————equation(2)
Substituting equation(2) in equation(1)
= > h + 50 = 90
= > h = 90 - 50 = 40
= >present age of the husband = 40

29. The average weight of 8 person’s increases by 2.5 kg when a new person comes in place of one of them weighing 65 kg. What is the weight of the new person?
A. 70                B. 75                C. 85            D 80
Answer : Option C
Explanation :
Total increase in weight = 8×2.5=20
If x is the weight of the new person, total increase in weight = x - 65
=> 20 = x - 65
=> x = 20 + 65 = 85
* MATHS (SOLVED IN STEPS ==> Ratio and Proportion
* MATHS (SOLVED IN STEPS ==> Progressions
* MATHS (SOLVED IN STEPS ==> Percentage
* MATHS (SOLVED IN STEPS ==> Surds and Indices
* MATHS (SOLVED IN STEPS ==> Calendar
* MATHS (SOLVED IN STEPS ==> Square and cube
* MATHS (SOLVED IN STEPS ==> Simplification
* MATHS (SOLVED IN STEPS ==> HCF & LCM 
* MATHS (SOLVED IN STEPS ==> Profit and Loss
* MATHS (SOLVED IN STEPS ==> Problems on Trains 
* MATHS (SOLVED IN STEPS ==> Problems on Age 
* MATHS (SOLVED IN STEPS ==> Pipe and Cisterns
* MATHS (SOLVED IN STEPS ==> ODD MAN
* MATHS (SOLVED IN STEPS ==> TIME & WORK



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