Home ≫ Arithmetic Aptitute ≫ Average ≫ Page 5
 
41. A person divides his total route of journey into three equal parts and decides to travel the three parts with speeds of 40, 30 and 15 km/hr respectively. Find his average speed during the whole journey.
  A.  24 km/hr
  B.  20 km/hr
  C.  26 km/hr
  D.  30 km/hr
     
   
View Answer

Shortcut:
If a person covers three equal distance at a speed of a km/hr, b km/hr and c km/hr respectively, then the average speed in covering the whole distance is
3 x a x b x c / ab + bc + ca
km/hr
Here, a = 40 km/hr, b = 30 km/hr, c = 15 km/hr
Using these values in shortcut, we get
3 x 40 x 30 x 15 / 40x30 + 30x15 + 15x40
=
3 x 40 x 30 x 15 / 2250
= 24 km/hr

42. A person covers 12 km at 3 km/hr, 18 km at 9 km/hr and 24 km at 4 km/hr. Then find the average speed in covering the whole distance.
  A.  8 km/hr
  B.  4.5 km/hr
  C.  6 km/hr
  D.  5 km/hr
     
   
View Answer

Shortcut:
If a person covers X km/hr at a km/hr and Y km at b km/hr and Z km at c km/hr, then the average speed in covering the while distnce is
X+Y+Z / X/a+ Y/b + Z/c
km/hr
Here, X = 12 km, a =3 km/hr, Y = 18 km, b = 9 km/hr, Z=24 km, c = 4 km/hr
Using these values in shortcut, we get
12+18+24 / 12/3 + 18/9 + 24/3
km/hr =
12+18+24 / 4 + 2 + 8
km/hr =
54 / 14
km/hr = 4.5 km/hr

43. A person runs the first 1/5th of the distance at 2 km/hr, the next one half at 3km/hr and the remaining distance at 1 km/hr. Find hhis average speed.
  A.  1
17 / 13
km/hr
  B.  1
13 / 17
km/hr
  C.  1.5 km/hr
  D.  3 km/hr
     
   
View Answer

Shortcut:
If a person covers Xth part of the distance at akm/hr, Yth part of the distance at b km/hr and the remaining Zth part at c km/hr, then his average speed is
1 / X/a+ Y/b + Z/c
km/hr
Zth part(remaining part) = 1 - (1/5 + 1/2 ) = 3/10
Here, Xth part = 1/5, a = 2 km/hr, Yth part = 1/2, b = 3 km/hr, Zth part = 3/10, c = 1 km/hr
Using these values in shortcut, we get
1 /
1/5 / 2
+
1/2 / 3
+
3/10 / 1

=
1 / 1/10 + 1/6 + 3/10
=
30 / 17
= 1
13 / 17
km/hr

44. The average salary of the entire staff in a office is Rs 120 per month. The average salary of officers is Rs 460 and that of non-officers is Rs 110. if the number of officers is 15, then find the number of non-officers in the office.
  A.  510
  B.  490
  C.  500
  D.  480
     
   
View Answer

Shortcut:
If the average value of all the members of a group is 'a', the average value of the first part of members is 'b' the averge value of the remaining part of members is 'c' and the number of the first part of members is 'z', then the number of the other part of members is
z(b - a) / a - c

Here, z = 15, a = 120, b = 460, c = 110
Using these values in shortcut, we get
15(460 - 120) / 120 - 110
= 510

45. The average age of all the students of a class is 18 years. The average age of boys of the class is 20 years and that of the girls is 15 years. If the number of girls in the class is 20, then find the number of boys in the class.
  A.  35
  B.  30
  C.  25
  D.  28
     
   
View Answer

Shortcut:
If the average value of all the members of a group is 'a', the average value of the first part of members is 'b' the average value of the remaining part of members is 'c' and the number of the remaining part of members is 'z', then the number of the first part of members is
z(a - c) / b - a

Here, z = 20, a = 18, b = 20, c = 15
Using these values in shortcut, we get
20(18 - 15) / 20 - 18
= 30

46. There were 35 studetns in a hostel. If the number of students increases by 7, the expenses of the mess increase by Rs 42 per day while the average expenditure per head diminishes by Re. 1. Find the original expenditure of the mess.
  A.  Rs 420
  B.  Rs 400
  C.  Rs 450
  D.  Rs 395
     
   
View Answer

Shortcut:
There were N students in a hostel. If the number of students increases by a, the expenses of the mess increasec by Rs b per day while the average expenditure per head diminishes by Rs c. The original expenditure is N
c(N + a)+b / a

Here, N=35, a = 7, b = 42, c = 1
Using these values in shortcut, we get
= 35 x
1(35 + 7) + 42 / 7
= 35 x
42 + 42 / 7
= 35 x
84 / 7
= 35 x 12 = Rs 420

47. Find the average of first 61 natural numbers.
  A.  36
  B.  28
  C.  33
  D.  31
     
   
View Answer

Shortcut:
The average of first 'n' natural numbers =
n + 1 / 2

Here, n = 61
Using the value of n in the shortcut we get: Average =
61 + 1 / 2
=
62 / 2
= 31

48. The average weight of 50 balls is 5 gm. If the weight of the bag be included the average weight increase by 0.05 gm. What is the weight of the bag?
  A.  8 gm
  B.  5 gm
  C.  7.55 gm
  D.  8.55 gm
     
   
View Answer

Shortcut:
The average weight of n balls is a gm. If the weight of the bag be included the average weight increases by b gm. The weight of the the bag will be
a + b x (Total number of objects)
Here, a = 5, b = 0.05 gm, Total no. of objects = n+1 (1 bag and n balls)
Using the value of n in the shortcut we get:
Weight of bag = 5 + 0.05 x 51 = 7.55 gm

49. Find the averge of first 101 natural numbers.
  A.  49
  B.  51
  C.  55
  D.  48
     
   
View Answer

Shortcut:
The average of first 'n' natural numbers =
n + 1 / 2

Here, n = 101
Using the value of n in the shortcut we get:
Average =
101 + 1 / 2
=
102 / 2
= 51

50. The average weight of 20 balls is 2 gm. If the weight of the bag be included the average weight increases by 0.02 gm. What is the weight of the bag?
  A.  2.42gm
  B.  1.42gm
  C.  3gm
  D.  1.5gm
     
   
View Answer

Shortcut:
The average weight of n balls is a gm. If the weight of the bag be included the average weight increases by b gm. The weight of the the bag will be
a + b x (Total number of objects)
Here, a = 5, b = 0.05 gm, Total no. of objects = n+1 (1 bag and n balls)
Using the value of n in the shortcut we get:
Weight of bag = 2 + 0.02 x (20+1) = 2 + (0.02 x 21) gm = 2 + 0.42 = 2.42 gm

Copyright © 2020-2022. All rights reserved. Designed, Developed and content provided by Anjula Graphics & Web Desigining .