3.Mallapragada's Mathematics ( Average -1)

ramakrishnamallapragada101@gmail.com

(AVERAGE)

Sl.No	Problems	Answers
1	Find the average of all prime numbers between 30 to 50
2	Find the average of 50 natural numbers
3	Find the average of first 30 multiples of 8
4	The average of 4 consecutive even numbers is 30, Find the largest of these numbers.
5	a,b,c,d,e, are five consecutive odd numbers their average is
6	The average of 7 consecutive numbers is 20. The largest of these numbers is
7	The average of five consecutive odd numbers is 61 . What is the difference between the highest and lowest numbers?
8	The average  average  weight of 10 oarsmen in a boat is increased by 1.8 Kg. when one of the crew, who weight  53 kg. is replaced by a new .  Find the weight of the new man.
9	The average weight of 8 persons increases b 2.5 kg when a new person comes in place of one of them weighting 65 kg. What might be the weight of the new person?
10	Of the three numbers, second is twice the first and is also thrice the third.  If the average of the three numbers is 44, find the largest number.
11	The average of 25 results is 18.  The average of the first twelve of them is 14 and that of last twelve is 17.  Find the thirteenth result.
12	The average of 11 results is 60.  If the average of first six results is 58 and that of the last six is 63, find the sixth result.
13	The average weight of A,B,C, id 45 kg. If the average weight of A and B be 40 Kg. and that of B And C be 43 Kg. find the weight of B.
14	The average age of a class of 39 students is 15 years. If the age of the teacher be included, then the average increases by 3 months. Find the age of the teacher.
15	The batsman makes a score of 87 runs in the 17th inning and thus increases his average by 3. Find his average after 17th inning.
16	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:
17	The average of first five multiples of 3 is
18	The average of eh first nine prime numbers is
19	If the mean of 5 observations x,x+2,x+4,x+6 and x+8 is 11, then the mean of the last three observations is:
20	The average of all odd numbers up to 100 is:
21	The sum of the three consecutive odd numbers is 38 more than the average of these numbers what is the first of these numbers?
22	The average of five numbers is 27 If one number is excluded the average becomes 25, The excluded number is:
23	The  average  age of 35 students in a class, is 16 years.  The average age of 21 students is 14 what is the average age of remaining 14 students?
24	The average score of a cricketer for ten matches is 38.9 runs.  If the average for the first six matches is 42, then find the average for the last four matches.
25	The average of ten numbers is 7.  If each number is multiplied by 12.  Then the average of the now set of number is:
26	The mean of 50 observations was 36.  It was found later that an observation 48 was wrongly taken as 23.  The corrected new mean is :
27	The average weight of A,B,C is 45 kg.  If the average weight. Of A and B be 40 Kg. and that of B and C be 43 Kg. then the weight of B is:
28	The average monthly income of P and Q is Rs. 5050. The average monthly income of Q & R is 6250 and the average monthly income of P and R is Rs. 5200.  The monthly income of P is
29	The average age of 36 students in a group is 14 years.  When teacher’s age is included to it, the average increases by one.  What is the teacher’s age in years?
30	A  cricketer  has a certain average for 10 innings.  In the eleventh inning. He scored 108 runs, thereby increasing his average by 6 runs.  His new average is:

                                                                                       

1	Find the average of all prime numbers between 30 to 50  ? Ans. There are 5 prime numbers  between 30 to 50           i.e. 31,37.41,43,47  Required average          31+37+41+43+47/5=199/5=39.8
2	Find the average of 50 natural numbers  ? Ans.sum of n natural numbers n(n+1)/2= Sum of         the 1st 50mnaturala numbers 50(50+1)/2 = 50          x 51/2 = 1275 == Required average  1275/50 =          25.5
3	Find the average of first 30 multiples of 8  ? Ans. Required average 8(1+2+3+…30)/30 =            8x30x31/2x30 = 4 x 31 =124
4	The average of 4 consecutive even numbers is 30, Find the largest of these numbers. Ans. X + (x+2)+ (x+4) + (x+6)/4 = 30          4x + 12/4 =30 4(x+3)/4 = 30          X+3 = 30 Therefore x = 27
5	a,b,c,d,e, are five consecutive odd numbers their average is Ans. a+(a+2)+(a+4)+(a+6)+(a+8)/5= (5a+ 20)/5          5(a+4)/5  Therefore  a=-4 (non of these )
6	The average of 7 consecutive numbers is 20. The largest of these numbers is Ans. a+(a+1)+(a+2)+(a+3)+(a+4)+ (a+5)+(a+6)/7=20           7a+21=140 7a= 119  a= 119/7 =17           Large number is a+6= 17 +6 = 23.
7	The average of five consecutive odd numbers is 61 . What is the difference between the highest and lowest numbers? Ans. a+(a+2)+(a+4)+(a+6)+(a+8)/5 = 61          A+4=61  Therefore a = 57
8	The average  average  weight of 10 oarsmen in a boat is increased by 1.8 Kg. when one of the crew, who weight  53 kg. is replaced by a new .  Find the weight of the new man. Ans.  Total weight increased = 1.8 x 10 = 18 Kg.           Weight of new men = 53 + 18 = 71 Kg.
9	The average weight of 8 persons increases b 2.5 kg when a new person comes in place of one of them weighting 65 kg. What might be the weight of the new person? Ans. Total weight increased = 2.5 x 8 = 20 Kg.           Weight of new men = 65 + 20 = 85 Kg.
10	Of the three numbers, second is twice the first and is also thrice the third.  If the average of the three numbers is 44, find the largest number. Ans. Let the third number is x, Then second          Number = 3x first No. 3x/2          Average: x + 3x + 3x/2 ={ (2x + 6x+  3x)/2}3) =               11x /2= 44 x3  == 11x = 88 x 3 = x=24              1st Number is 3x/2= 3x24/2=3x12=36              2nd  No. 3x = 3 x 24= 72 (largest number )
11	The average of 25 results is 18.  The average of the first twelve of them is 14 and that of last twelve is 17.  Find the thirteenth result. Ans. Clearly, thirteenth result: (sum of 25 results)-          (sum of 24 results) =                                                                       (18 x 25) – {(14 x12)+(17x12)} =                                   450 – (168+204)= 45-  372= 78
12	The average of 11 results is 60.  If the average of first six results is 58 and that of the last six is 63, find the sixth result. Ans. Sixth result = (58 x 6)+ ( 63x6) – (60x 11)=          (348 + 378) -660 =66
13	The average weight of A,B,C, is 45 kg. If the average weight of A and B be 40 Kg. and that of B And C be 43 Kg. find the weight of B. Ans. Let the ABC is represents the individual          weights. Then A+B+C= 45 x 3 = 135 Kg.          A + B = 40 x 2 = 80 Kg., B + C = 43 x 2= 86          B = (A + B)+ (B + C)  -(A+B+C)  =(80+86)-135 Kg           B = 166-135= 31Kg
14	The average age of a class of 39 students is 15 years. If the age of the teacher be included, then the average increases by 3 months. Find the age of the teacher. Ans. Total age of 39 persons = (39 x 15 )years          585 years           Average age of40 persons = 15years 3 months          = 15 3/12= 151/4 =61/4 years          = Total age of 40 persons = (61/4 x 40 }=610             Years = Age of the teacher = 610 – 585 =25
15	A batsman makes a score of 87 runs in the 17th inning and thus increases his average by 3. Find his average after 17th inning. Ans. Let the average after 17th inning = x          Let the average of 16th innings = (x-3)           = 16(x-3)+87=17x   Therefore 16x-48+87=17x           16x + 39 = 17x   Therefore x=39
16	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: Ans. Let the ratio of be K:1 then          = K x 16.4 + 1x 15.4 –(K+1) x 15.8          =16.4K-15.8K=15.8-15.4         = k=0.4/0.6 = 2/3          Required ratios : 2/3:1 = 2:3
17	The average of first five multiples of 3 is Ans. average = 3(1+2+3+4+5)/5 = 45/5=9
18	The average of eh first nine prime numbers is Ans. 2+3+5+7+11+13+17+19+23/9 = 100/9 =11.11
19	If the mean of 5 observations x,x+2,x+4,x+6 and x+8 is 11, then the mean of the last three observations is: Ans. x +(x+2)+(x+4)+(x+6) +( x+8)/5=11         = 5x+20=55,  5x= 55-20 x = 35/5=7          The numbers are 7,9,11,13,15          Required last three (11+13+15)/3=39/3=13
20	The average of all odd numbers up to 100 is: Ans. 1+3+5+7…..97+99          (1+99),(3+97),(5+95) …..up to 25 pairs           100+100+100 (25 times) =2500           Average = 2500/50 = 50
21	The sum of the three consecutive odd numbers is 38 more than the average of these numbers what is the first of these numbers? Ans. lat the number be x,x+2,x+4          Then   (x +x+2 +x+4)-( x+x+2 +x+4)/3 =38         (3x+6)- (3x+6)/3 =38, 9x+18 – 3x-6=114         6x = 114-12=102  Therefore x = 17
22	The average of five numbers is 27 If one number is excluded the average becomes 25, The excluded number is: Ans. (5x27)-(4x25)=135-100=35
23	The  average  age of 35 students in a class, is 16 years.  The average age of 21 students is 14 what is the average age of remaining 14 students? Ans. Sum of the age of 14 students=                                    (16x35)-(14x21)=560-294=266          Required average 266/14 = 19 years
24	The average score of a cricketer for ten matches is 38.9 runs.  If the average for the first six matches is 42, then find the average for the last four matches. Ans. Required average. (38.9 x 10)-42 x 6/4=137/4
25	The average of ten numbers is 7.  If each number is multiplied by 12.  Then the average of the now set of number is: Ans. Average 10 numbers = 7 Sum of these 10 numbers = 10 x 7 = 70 12x(1)+ 12x(2)+…….12 x (10)/10 84
26	The mean of 50 observations was 36.  It was found later that an observation 48 was wrongly taken as 23.  The corrected new mean is : Ans. Correct sum : 50 x 36 + 48 – 23 = 1825 Correct mean = 1825/ 50  = 36.5
27	The average weight of A,B,C is 45 kg.  If the average weight. Of A and B be 40 Kg. and that of B and C be 43 Kg. then the weight of B is: Ans. A,B,C, represents their weights. A + B + C = 45 x 3 = 135 ………….. i A + B = 40 x 2 = 80  …………………….ii B + C = 43 x 2 = 86 …………… iii  Adding II and III A + 2B + C = 166 sub. (i) from (iv) weight B. 31. B weight 31 kg.
28	The average monthly income of P and Q is Rs. 5050. The average monthly income of Q & R is 6250 and the average monthly income of P and R is Rs. 5200.  The monthly income of P is Ans. P.Q.R represent their respective monthly incomes. Then we have P+Q = 5050 x 2 = 10100  ………………i Q + R = 6250 2= 12500  ………………..ii P + R = 5200 x 2 = 10400  ………………iii Adding I,ii,iii we get 2(P+Q+R)= 33000 P + Q + R = 16500, p = 4000
29		The average age of 36 students in a group is 14 years.  When teacher’s age is included to it, the average increases by one.  What is the teacher’s age in years? Ans.  Average of teacher = (37 x 15 -36 x 14)= 555-504 =51years
30		A  cricketer  has a certain average for 10 innings.  In the eleventh inning. He scored 108 runs, thereby increasing his average by 6 runs.  His new average is: Ans. Let average for 10 innings be x then 10x+108/11=x+6, 10x+108=11x + 66 X= 42, There fore average = x + 6 = 42 + 6 = 48.