The average age of a group of men is 20 years. Two men whose ages are 23 years and 27 years joined the group. The average age o the group increased by a prime number. The number of men in the original group is
Answer: A Let the number of men in the original group be N The total ages of the original group = 20N years. The total age of the new group = 20N+50 years. Let increase in the average be x years 20N+50 = (N+2)(20+x) => 10 = x(N+2). Therefore x and N+2 must be factors of 10. As x is prime x can be 2 or 5. If x=2, N=3 X=5, N=0 which is not possible. Thus, N=3.
Q. No. 20:
The average of the ages of a man and his only son exceeds the average of the ages of his wife and his son by 25%. The age of his son is 30 years less than the age of his wife whose age is 10 year less than his age. Find the age of his son (in years)
Answer: A Let the present ages of the father, his only son and his wife be fyears, s years and m years respectively. (f+s)/2 = 5/4*((s+m)/2) 4(f-m) = s+m f-m =10 and m-s = 30 On solving these equations we get s=5.
Q. No. 21:
The average of 3 toys X,Y and Z is 84 kg. Another toy P joins the group and the average now becomes 80kg. If another toy Q, whose weight is 3kg more than that of P, replaces X then the average weight of Y,Z,P and Q becomes 79kg. The weight of X is
Answer: C Total weight of X,Y and Z = 84*3 = 252 kg Total weight of X,Y,Z and P = 80*4 = 320kg weight of P = 320-252 = 68kg weight of Q = 68+3 = 71 kg Total weight of Y,Z,P and Q = 79*4=316kg Total weight of Y,Z and P = 316-71 = 245 kg Weight of X = 320-245 = 75kg.
Q. No. 22:
In a cricket eleven, the average age of eleven players is 28 year. Out of these, the average ages of three groups of three players each are 25 year, 28 year and 30 year respectively. If in these groups, the captain and the youngest players are not included and the captain is eleven years older than the youngest player, what is the age of the captain?
Answer: C Total age of 11 players = 308 year Total age of 9 players in a group of 3 = (25*3 +28*3 + 30*3) = 249 year. Total age of remaining 2 players = 308-249 = 59 year Let the age of youngest player be x year, then age of captain = x+11 x+(x+11) =59 => x= 24 years. Therefore, age of captain = 24+11 = 35 year.
Q. No. 23:
The average weight of a class of 29 students is 40kg. If the weight of teacher be included, the average rises by 0.5 kg. What is the weight of the teacher?
Answer: D Total weight of 29 students = 29*40 =1160kg Total weight including teacher = 30*40.5 = 1215 kg Weight of teacher = 1215-1160 = 55 kg.
Q. No. 24:
The average age of 8 persons in a committee is increased by 2 year when two men aged 35 year and 45 year are substituted by two women. Find the average age of the two women.
Answer: A Total increase in age of 8 persons =16 year. Clearly, the total age of two women is 16 year more than total age of two men. Hence, total age of women = (35+45)+16 = 96 year. Therefore, average = 96/2 = 48.