How to solve problems using chain rule

In a dairy farm, 40 cows eat 40 bags of husk in 40 days. In how many days one cow will eat one bag of husk?

a.       1              b.  40                     c. 20                       d. 26

Answer:

What do we need to find? ... the number of days.

So, first record the day data given =  40 x ..................       (1)

Next go to the other variables. First, consider the number of cows.

Since the number of cows is decreasing, the husk will last more number of days. Whenever there is more, your multiplication factor should be greater than 1. So, (40/1)  ------ (2)

Second variable is bags of husk

Since the number of bags of husk is decreasing, the husk will last less number of days. Whenever there is less, your multiplication factor should be less than 1. So, (1/40) ------ (3)

Therefore, total number of days = 40 x (40/1) x (1/40) = 40 days   ...............(1) x (2) x (3)

Answer is B.

In a camp, there is a meal for 120 men or 200 children. If 150 children have taken the meal, how many men will be catered to with remaining meal?

a)      50                           b) 40                      c) 30                       d) 10

Answer:

150 children = 120 x (150/200) men = 90 men

So, balance number of men = 120 – 90 = 30

 3 pumps, working 8 hours a day, can empty a tank in 2 days. How many hours a day should 4 pumps work in order to empty the tank in 1 day?

a)      10                           b) 12                      c) 8                         d) 15

Answer:

= 8 x (3/4) x(2/1) = 12 hours

Note the factor   ----  ¾

More number of pumps will take less number of hours to do the job. less means fraction should be less than 1. So, ¾ and not 4/3.

Now, note the factor   2/1

In job is to be completed in less number of days, more hour of work is required. More means the fraction should be more than 1. So, 2/1 and not ½.

Remember, that relationship has to be established strictly with the variable you have to find.

21 goats eat as much as 15 cows. How many goats eat as much as 35 cows?

a)      49                           b)32                       c)36                        d)41

Answer:

 21 x (35/15) = 49

More number of cows means more the number of goats. So, the multiplication factor should be more than 1. So, fraction will be (35/15) and not (15/35)

A fort had provision of food for 150 men for 45 days. After 10 days, 25 men left the fort. Find out the number of days for which the remaining food will last.

a)      45                           b) 42                      c)40                        d)38

Answer:

We can rewrite the above question as, “the fort has provision for 150 men for (45 – 10 = 35) days. How many days will the provision last for (150 – 25 = 125) men”

 35 x (150/125) = 42 days

Answer is b

Note: less number of men means provision will last more number of days. More means fraction should be greater than 1. So, fraction is (150/125) and not (125/150).