(1) The average of 17 results is 38. If the average of the first 9 results is 39 and that of the last 9 results is 36, then find the 6th result.
a) 37 b) 29 c)31 d)27
Sum of series = 17*38 = 646
Sum of first 6 results = 9*39 = 351
Sum of last 6 results = 9*36 = 324
Hence, Sum of 9th result = (351+324) – 646 = 29
(2) There are three sections in a class, whose average marks are 53, 49 and 63. If the number of students in these sections is 63, 49 and 53, respectively, then find the approximate average marks of the entire class.
a) 56 b) 54 c)55 d)52
Total marks of 1st Section = 53*63= 3339
Total marks of 2nd Section = 49*49 = 2401
Total marks of 3rd Section = 63*53 = 3339
Average of all three sections = (3339+2401+3339)¸/(53+49+63) = 55.02
(3) The average of 45 2/3, 35 3/4 , 28 4/5, 32 5/6 is
a) 35 (61/80) b) 35 (31/60) c) 35 (31/80) d)35 (51/120)
Average = [ (45+35+28+32) +( 2/3 +3/4 + 4/5 + 5/6 ) ] ¸ 4
[140 + 3 (1/20) ] /4 = 35 + 61/80 = 35 (61/80)
(4) A motorist covered the first 32 km of his journey in 45 minutes and the remaining 38 km in 25 minutes. His average speed (in km/hr) is
a) 40 b) 80 c) 50 d) 60
Total Distance = 32+38 = 70
Total Time = 45/60 + 25/60 = 7/6
Average Speed = 70/(7/6) = 60
(5) The average marks scored by 75 students in a class were 26.4. The marks of the first fifteen students were altered from 25 to 17 and that of the last fifteen students from 13 to 23. What were the new average marks of the class?
a) 26.8 b) 28 c) 25.6 d) 27.4
Total marks of the class = 75*26.4 =1980
Marks of first fifteen student = 15*25 =375
Marks of last fifteen student = 15*13 = 195
Altered Marks of first fifteen student = 15*17 = 255
Altered Marks of last fifteen student = 15*23 = 345
Resultant altered Marks = (375+195)-(255+345) = -30
New average = (1980+30)¸75 = 26.8 OR 30/75 = 0.4 , 26.4+0.4 = 26.8
(6) The temperature of a city on Monday was 37.35oC. For the next three days, the temperature was 1.75oC more than that on the previous day. From Friday to Saturday, the temperature was 1.25oC less than that on the previous day. Find the average temperature of the city from Monday to Saturday.
a) 39.325 b) 40.225 c) 41.750 d) 39.450
Temperature on Monday = 37.35
Temp on Tuesday, wed, Thu = 39.10, 40.85, 42.60
Temp on Fri, Sat = 41.35, 40.10
Sum of Temp on Monday to Saturday = 4/2 [ 2*37.35 + 3*1.75 ] + 81.45 = 159.90 + 81.45 = 241.35
Average = 241.35/6 = 40.225
(7) The average weight of 85 balls is 8 g. If the weight of a bag is included, the average weight increases by 0.09 g. What is the weight of the bag?
a) 18.54 b) 17.96 c) 15.74 d) 16.24
Total weight of the balls = 85*8 =680
Total weight of the balls with bag = 86*8.09 = 695.74
Weight of the bag = 695.74-680 = 7.65 OR 85*0.09 = 15.74
(8) Ross scored a total of 299 points in 23 basketball games. Joey played 7 fewer games than Ross and his scoring average was 1.5 points per game higher than Ross's scoring average. How many points in total did Joey score?
a) 276 b) 247 c) 221 d) 232
If Ross scored 299 points in 23 games, this implies that he averages or 13 points per game.
Joey must then have averaged 14.5 points in each of the 16 games he played.
In total, he scored = 14.5 × 16 = 232 points
(9) The average speed of a cyclist who covers first, second and third km at speeds of 9km/hr, 12 km/hr and 15 km/hr, respectively, is
a) 11.48 km/h b) 10.68 km/h c) 13.54 km/h d) 12.86 km/h
a) 37 b) 29 c)31 d)27
Sum of series = 17*38 = 646
Sum of first 6 results = 9*39 = 351
Sum of last 6 results = 9*36 = 324
Hence, Sum of 9th result = (351+324) – 646 = 29
(2) There are three sections in a class, whose average marks are 53, 49 and 63. If the number of students in these sections is 63, 49 and 53, respectively, then find the approximate average marks of the entire class.
a) 56 b) 54 c)55 d)52
Total marks of 1st Section = 53*63= 3339
Total marks of 2nd Section = 49*49 = 2401
Total marks of 3rd Section = 63*53 = 3339
Average of all three sections = (3339+2401+3339)¸/(53+49+63) = 55.02
(3) The average of 45 2/3, 35 3/4 , 28 4/5, 32 5/6 is
a) 35 (61/80) b) 35 (31/60) c) 35 (31/80) d)35 (51/120)
Average = [ (45+35+28+32) +( 2/3 +3/4 + 4/5 + 5/6 ) ] ¸ 4
[140 + 3 (1/20) ] /4 = 35 + 61/80 = 35 (61/80)
(4) A motorist covered the first 32 km of his journey in 45 minutes and the remaining 38 km in 25 minutes. His average speed (in km/hr) is
a) 40 b) 80 c) 50 d) 60
Total Distance = 32+38 = 70
Total Time = 45/60 + 25/60 = 7/6
Average Speed = 70/(7/6) = 60
(5) The average marks scored by 75 students in a class were 26.4. The marks of the first fifteen students were altered from 25 to 17 and that of the last fifteen students from 13 to 23. What were the new average marks of the class?
a) 26.8 b) 28 c) 25.6 d) 27.4
Total marks of the class = 75*26.4 =1980
Marks of first fifteen student = 15*25 =375
Marks of last fifteen student = 15*13 = 195
Altered Marks of first fifteen student = 15*17 = 255
Altered Marks of last fifteen student = 15*23 = 345
Resultant altered Marks = (375+195)-(255+345) = -30
New average = (1980+30)¸75 = 26.8 OR 30/75 = 0.4 , 26.4+0.4 = 26.8
(6) The temperature of a city on Monday was 37.35oC. For the next three days, the temperature was 1.75oC more than that on the previous day. From Friday to Saturday, the temperature was 1.25oC less than that on the previous day. Find the average temperature of the city from Monday to Saturday.
a) 39.325 b) 40.225 c) 41.750 d) 39.450
Temperature on Monday = 37.35
Temp on Tuesday, wed, Thu = 39.10, 40.85, 42.60
Temp on Fri, Sat = 41.35, 40.10
Sum of Temp on Monday to Saturday = 4/2 [ 2*37.35 + 3*1.75 ] + 81.45 = 159.90 + 81.45 = 241.35
Average = 241.35/6 = 40.225
(7) The average weight of 85 balls is 8 g. If the weight of a bag is included, the average weight increases by 0.09 g. What is the weight of the bag?
a) 18.54 b) 17.96 c) 15.74 d) 16.24
Total weight of the balls = 85*8 =680
Total weight of the balls with bag = 86*8.09 = 695.74
Weight of the bag = 695.74-680 = 7.65 OR 85*0.09 = 15.74
(8) Ross scored a total of 299 points in 23 basketball games. Joey played 7 fewer games than Ross and his scoring average was 1.5 points per game higher than Ross's scoring average. How many points in total did Joey score?
a) 276 b) 247 c) 221 d) 232
If Ross scored 299 points in 23 games, this implies that he averages or 13 points per game.
Joey must then have averaged 14.5 points in each of the 16 games he played.
In total, he scored = 14.5 × 16 = 232 points
(9) The average speed of a cyclist who covers first, second and third km at speeds of 9km/hr, 12 km/hr and 15 km/hr, respectively, is
Average Velocity =(3*9*12*15)/((108+180+135))= 11.48 km/h
(10) The average age of a class of 47 students and a teacher named wayne reduces by 0.4 years when the age of the teacher is not included. If the average age of the class and the teacher is 25 years, then find the age of wayne.
a) 45.2 b) 44.8 c) 43.8 d) 46.6
Age of teacher = Total age of (students + teacher) - Total age of students
= 48 × 25 – 47 × 24.6
= 1200 – 1156.2 = 43.8 years