Chain Rule

Chain Rule

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Question 1
3 pumps, working 8 hours a day, can empty a tank in 2 days. How many hours a day must 4 pumps work to empty the tank in 1 day?
A
9
B
10
C
11
D
12
Question 1 Explanation: 
Let the required number of working hours per day be x. More pumps, Less working hours per day (Indirect Proportion) Less days, More working hours per day (Indirect Proportion) Pumps 4 : 3 :: 8 : x Days 1 : 2 4 x 1 x x = 3 x 2 x 8 x = (3 x 2 x 8)/(4) x = 12.
Question 2
A fort had provision of food for 150 men for 45 days. After 10 days, 25 men left the fort. The number of days for which the remaining food will last, is:
A
29
B
39
C
42
D
54
Question 2 Explanation: 
After 10 days : 150 men had food for 35 days. Suppose 125 men had food for x days. Now, Less men, More days (Indirect Proportion) 125 : 150 :: 35 : x 125 x x = 150 x 35 x = ((150 x 35)/125) x = 42.
Question 3
If a quarter kg of potato costs 60 paise, how many paise will 200 gm cost?
A
48 paise
B
54 paise
C
56 paise
D
72 paise
Question 3 Explanation: 
Let the required weight be x kg. Less weight, Less cost (Direct Proportion) 250 : 200 :: 60 : x 250 x x = (200 x 60) x= (200 x 60)/250 x = 48.
Question 4
A wheel that has 6 cogs is meshed with a larger wheel of 14 cogs. When the smaller wheel has made 21 revolutions, then the number of revolutions mad by the larger wheel is:
A
4
B
9
C
12
D
16
Question 4 Explanation: 
Let the required number of revolutions made by larger wheel be x. Then, More cogs, Less revolutions (Indirect Proportion) 14 : 6 :: 21 : x 14 x x = 6 x 21 x = ((6 x 21)/14) ==> 9.
Question 5
A flagstaff 17.5 m high casts a shadow of length 40.25 m. The height of the building, which casts a shadow of length 28.75 m under similar conditions will be:
A
10 m
B
12.5 m
C
17.5 m
D
21.25 m
Question 5 Explanation: 
Let the height of the building x metres. Less lengthy shadow, Less in the height (Direct Proportion) 40.25 : 28.75 :: 17.5 : x 40.25 x x = 28.75 x 17.5 x = (28.75 x 17.5)/40.25 ==> x = 12.5
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