Home ≫ Arithmetic Aptitute ≫ Ratio and Proportion ≫ Page 4
31. A can do a piece of work in 24 days. B is 20% less efficient than A. Find the number of days it takes B to do the same piece of work.
  A.  30 days
  B.  25 days
  C.  28 days
  D.  40 days
     
   
View Answer

shortcut method:

100 / 100-20
x 24 =
100 / 80
x 24 = 30 days

32. In 24 litres mixture of milk and water the ratio of milk and water is 3 : 1. How much water should be added in the mixture so that the ratio of milk to water becomes 2 : 1?
  A.  5 litres
  B.  3 litres
  C.  1 litres
  D.  8 litres
     
   
View Answer

Short cut method:

x(ad-bc) / c(a+b)
x=24 a=3 b=1 c=2 d=1 Applying these values in the short cut, we get:
24(3 x 1 - 1 x 2) / (3+1)2
=
24 / 8
= 3 litres

33. In 18 litres mixture of milk and water, the ratio of milk and water is 7 : 3. Find the quantity of water to be added in the mixture in order to make this ratio 3 : 7.
  A.  21 litres
  B.  24 litres
  C.  27 litres
  D.  26 litres
     
   
View Answer

Short cut method:

x(ad-bc) / c(a+b)
x=18 a=7 b=3 c=3 d=7 Applying these values in the short cut, we get:
18(7 x 7 - 3 x 3) / (7+3)3
= 24 litres

34. A mixture contains milk and water in the ratio of 3 : 2. If 5 litres of water is added to the mixture, milk and water in the mixture become equal. Find the quantities of milk and water in the mixture.
  A.  Milk quantiy:15 litres; Water quantity: 10 litres
  B.  Milk quantiy:10 litres; Water quantity: 15 litres
  C.  Milk quantiy:20 litres; Water quantity: 15 litres
  D.  Milk quantiy:10 litres; Water quantity: 20 litres
     
   
View Answer

Short cut method: Quantity of milk in the mixture =

ax / c-b
Quantity of water in the mixture =
bx / c-b
x=4 a=3 b=2 c=3 Applying these values in the short cut, we get: Quantity of milk =
ax / c-b
=
3 x 5 / 3-2
= 15 litres Quantity of water =
bx / c-b)
=
2 x 5 / 3-2
= 10 litres

35. A mixture contains milk and water in the ratio of 8 : 3. On adding 4 litres of water, the ratio of milk to water becomes 2 : 1. Find the quantities of milk and water in the mixture.
  A.  Milk quantiy:11 litres; Water quantity: 13 litres
  B.  Milk quantiy:32 litres; Water quantity: 12 litres
  C.  Milk quantiy:30 litres; Water quantity: 14 litres
  D.  Milk quantiy:12 litres; Water quantity: 32 litres
     
   
View Answer

Short cut method: Quantity of milk in the mixture =

ax / c-b
Quantity of water in the mixture =
bx / c-b
To follow the above theorem, we change the ratios in the form a:b and a:c. Then the ratios can be written as 8:3 and 8:4 x=4 a=8 b=3 c=4 Applying these values in the short cut, we get: Quantity of milk =
ax / c-b
=
8 x 4 / 4-3
= 32 litres Quantity of water =
bx / c-b
=
3 x 4 / 4-3
= 12 litres

36. An amount is to divided between two mens in the ratio of 3 : 5. If the share of one person is Rs 10 less than that of the other, find the amount.
  A.  Rs 40
  B.  Rs 25
  C.  Rs 45
  D.  Rs 30
     
   
View Answer

Short cut method:

Total sum / 10
=
3 + 5 / 5-3
∴ Total sum =
8 / 2
x 10 = Rs 40

37. The prices of a bike and bicycle are in the ratio of 9 : 5. If a bike cost Rs 4000 more than a bicycle, find the price of the bicycle.
  A.  Rs 4000
  B.  Rs 6000
  C.  Rs 3000
  D.  Rs 5000
     
   
View Answer

Short cut method:

Total sum / 4000
=
9 + 5 / 9 - 5
∴ Total sum =
14 / 4
x 4000 = Rs 14000

38. The sides of a hexagon are enlarged by 3 times. Find the ratio of the areas of the new and old hexagons.
  A.  9 : 1
  B.  1 : 6
  C.  1 : 9
  D.  2 : 3
     
   
View Answer

Shortcut method: In any two 2-dimensional figures, if the corresponding sides are in the ratio a:b, then their areas will be in the ratio a2:b2. we see that the ratio of the corresponding sides of the two hexagons is a:b = 1:3 By using the above short cut, we get The ratio of their areas is a2:b2 = 12:32 = 1:9

39. The ratio of the diagonals of two squares is 3 : 1. Find the ratio of their areas.
  A.  3 : 1
  B.  9 : 1
  C.  1 : 3
  D.  1 : 9
     
   
View Answer

Let ratio of the diagonals of two squares be a:b = 3:1 then, by using the short cut method, the ratio of areas of two squares be a2:b2 = 32:12 = 9:1

40. The ratio of the radius(or diameter or circumference) of two circles is 1 : 4. Find the ratio of their areas.
  A.  1 : 16
  B.  2 : 8
  C.  1 : 12
  D.  2 : 4
     
   
View Answer

Let ratio of the radius/diameter/circumference of two circle be a:b = 1:4 then, by using the short cut method, the ratio of areas of two squares be a2:b2 = 12:42 = 1:16

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