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1. Find the ratio compounded of the four ratios: 4 : 3, 9 : 13, 26 : 5 and 2 : 15
  A.  
25 / 16
  B.  
16 / 25
  C.  
4 / 5
  D.  
5 / 4
     
   
View Answer

The required ratio =
4 x 9 x 26 x 2 / 3 x 13 x 5 x 15
=
16 / 25

2. Find the fourth proportional to the numbers 6, 8 and 15
  A.  20
  B.  22
  C.  17
  D.  25
     
   
View Answer

Let a be the fourth proportional, then 6 : 8 = 15 : a

∴ a =
8 x 15 / 6
= 20

3. What should come in place of the question mark(?)
28 / ?
= 
? / 112
  A.  80
  B.  84
  C.  130
  D.  56
     
   
View Answer

Let a be the second and third proportional, then
28 : a = a : 112
a2 = 28 x 112
a = √(28 x 112)
a = 56

4. If 15 books cost Rs 35, what is the cost of 21 books?
  A.  Rs 51
  B.  Rs 49
  C.  Rs 29
  D.  None of the above
     
   
View Answer

Let the required cost/price be a.
More books → more price.
Thus the two quantities are direct proportional to each other.

Books 15(x1) 21(x2)
Price 35(y1) a(y2)
x1 / y1
=
x2 / y2

⇒
15 / 35
=
21 / a

⇒ a =
35 x 21 / 15
= 7 x 7 = Rs 49

5. If 15 men can reap a field in 28 days in how many days will 5 men reap it?
  A.  84 days
  B.  48 days
  C.  34 days
  D.  82 days
     
   
View Answer

Let the required number of days be a.
Less men → more days.
Thus the two quantities are inversely proportional to each other.

Men 15 (x1) 5 (x2)
Days 28 (y1) a (y2)

x1y1= x2y2
⇒ 15 x 28 = 5 x a
⇒ a =
15 x 28 / 5
= 3 x 28 = 84 days

6. A fort had provisions for 150 mens for 45 days. After 10 days, 25 men left the fort. How long will the food last at the same rate for the remaining men?
  A.  45 days
  B.  15 days
  C.  40 days
  D.  42 days
     
   
View Answer

The remaining food would last for 150 men for (45 - 10) = 35 days
Now, 25 men have gone out, the ramaining food would last for a longer period.
Hence, by the rule of three, we have the following relationship.
125 men : 150 men = 35 days : required number of days
∴ required number of days = (150 x 35)/125 = 42 days.
Let the required number of days be a.
Less men → more days.
Thus the two quantities are inversely proportional to each other.

Men 125 (x1) 150 (x2)
Days 35 (y1) a (y2)
x1y1= x2y2
⇒ 125 x 35 = 150 x a
⇒ a =
125 x 35 / 5
= 3 x 28 = 84 days

7. If 8 men can reap 80 hectares in 24 days, how many hectares can 36 men reap in 30 days?
  A.  380 hectares
  B.  320 hectares
  C.  360 hectares
  D.  300 hectares
     
   
View Answer

We can solve this question in two steps: 1st step
If 8 men can reap 80 hectares, then how many hectares can 36 men reap?
8 men: 36 men = 80 hectares : the required number of hectares

∴ required number of hectares =
36 x 80 / 8
= 360 hectares

2nd step:
If 360 hectares can be reaped in 24 days, how many hectares can be reaped in 30 days?
24 days : 30 days = 360 hectares : the required number of hectares.
∴ the required number of hectares =
30 x 360 / 24
= 450

8. If 360 hectares can be reaped in 24 days, How many hectares can be reaped in 30 days?
  A.  550 hectares
  B.  450 hectares
  C.  400 hectares
  D.  Nove of the above
     
   
View Answer

9. If Raju can walk a certain distance in 50 days when he takes rest 9 hours each day, how long will it take him to walk twice as far if he walks twice as fast and rests twice as long each day?
  A.  125
  B.  135
  C.  140
  D.  115
     
   
View Answer

In the first case Raju walks (24 - 9) = 15 hours each day.
On the 2nd Raju walks (24 - 18) i.e 6 hours each day
Now we have the following proportion.

distance 1:2
rate  2:1
hours  6:15 		} :: 50 days: required no. of days
∴ required number of days =
2 x 1 x 15 x 50 / 1 x 2 x 6
= 125

10. A garrison of 2200 men is provisioned for 16 weeks at the rate of 45 dag per diem per man. How many men must leave so that the same provisions may last 24 weeks at 33 dag per diem per man?
  A.  205
  B.  210
  C.  190
  D.  200
     
   
View Answer

per diem means per day.
2200 men provisioned for 16 weeks at 45 dag per day per man
? men provisioned for 24 weeks at 33 dag per day per man.
more weeks-->less men
less dag --->more men
We have the following proportion.

weeks 24:16
dag 33:45 		} :: 2200 men: required no. of men
∴ required number of men =
16 x 45 x 2200 / 24 x 33
= 2000
Hence (2200 - 2000) i.e 200 men must leave.

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