## Aptitude question and answer on Average

In this section we are going to discuss about average problems. Not just the overview of the topic, but also you are going to learn the important formulas on average along with explanation which is easy to understand.

 1 After replacing an old member by a new member, it was found that the average age of five members of a club is the same as it was 3 years ago. What is the difference between the ages of the replaced and the new member ? A.    15 years B.    10 years C.    6 years D.    3 years Answer : A.  15 years Explanation: Age decreased =(5 X 3) Years = 15 years. So, The required difference = 15 years. Discuss 2 India shooting team of 8 persons joins in a shooting competition.Santosh scored 84 points.If he had scored 92 points, the average score for team would have been 84. The number of points, the team scored , was A.    672 B.    665 C.    645 D.    588 Answer : B.   665 Explanation: Let the total score be . $\dot{..}$  ${x+92-85 \over8}=84$ => x+7=672 => x= 665. Discuss 3 The average weight of 8 men is increased by 1.5 kg when one of the men who weights 65kg is replaced by a new man. The weight of the new man is A.    76 kg B.    76.5 kg C.    76.7 kg D.    77 kg Answer : D.  77 kg Explanation: Total weight increased = (8 x 1.5) kg= 12 kg. Weight of new man = (65+12) kg = 77 kg. Discuss 4 The average of 5 numbers is 7. When 3 new numbers are added, the average of the eight number is 8.5. The average of the three new numbers is A.    11 B.    7.75 C.    8.5 D.    7 Answer : A.  11 Explanation: Sum of three new numbers = $(8 \times 8.5 - 5 \times 7)$=33. $\dot{..}$ There Average =$33 \over 3$=11. Discuss 5 The average age of boys in the class is twice the number of girls in the class. If the ration of boys and girls in the class of 36 be 5:1, what is the total of the ages (in years) of the boys in the class ? A.    380 B.    342 C.    372 D.    360 Answer : D.  360 Explanation: Number of boys = $\bigg(36 \times {5 \over 6}\bigg) =30$ Number of girls = 6. Average age of boys= (2 x 6)=12 years. $\dot{..}$ Total age of boys = (30 x12) years= 360 years Discuss 6 The average age of a class is 15.8 years. The average age of the boys in the class is 16.4 years while that of the girls is 15.4 years. What is the ration of boys to girls in the class ? A.    1 : 2 B.    3 : 4 C.    3 : 5 D.    2 : 3 Answer : D.  2 : 3 Explanation: Let the ratiobe k : 1 . Then , $k \times 16.4 \div 1 \times 15.4=(k+1) \times15.8$ Or  $(16.4 -15.8)k=(15.8-15.4)$ Or $k={0.4 \over 0.6}={2 \over 3}$ $\dot{..}$ Required ratio = ${2 \over 3}:1$= 2 : 3 Discuss 7 The average of 5 consecutive numbers is n.If the next two numbers are also included, the average will A.    increase by 1 B.    remain the same C.    increase by 1.4 D.    increase by 2 Answer : A.  increase by 1 Explanation: Let 5 consecutive numbers be x, x+1, x+2 , x+3 , and x+4 Their average = ${5x+10 \over5}=(x+2).$ Average of numbers = $(5x+10)+(x+5)+(x+6) \over 7$                               =$7x+21 \over 7$=$(x+3).$ So, the average increased by 1. Discuss 8 The average weight of 3men A,B and C is 84 kg.Another man D joins the group and the average now becomes 80 kg. If another man E, whose weight is 3 kg more  than that of D, replaces A then the average weight of B,C,D and E becomes 79 kg. The weight of A is A.    70 kg B.    72 kg C.    75 kg D.    80 kg Answer : C.  75 kg Explanation: A+B+C=(84 x 3) = 252 kg, A+B+C+D=(80 x 4)= 320 kg. $\dot{..}$ D=(320-252) kg = 68 kg, E= (68+3) kg = 71 kg. B+C+D+E = (79 x 4) = 316 kg. Now  (A+B+C+D)-(B+C+D+E) =(320-316) kg=4 kg. $\dot{..}$  A-E = 4 => A =(4+E) = 75 kg. Discuss