Chain Rule Questions from Pitambar Lal ( with solution)
Showing posts with label chain rule. Show all posts
Showing posts with label chain rule. Show all posts
Friday, August 1, 2014
how to solve chain rule problems
A garrison had provisions for a certain
number of days. After 10 days, 1/5 of the men desert and it is found that the
provisions will now last just as long as before. How long was that?
a)
50 days b) 30 days c) 40 days d) 60 days
Answer:
Let “x” be the number of days the
provisions would last for the garrison of “y” men
We can re phrase the question
now.
“ there is provision for y men
for ( x – 10) days, and there is provision for ( y – y/5 = 4y/5) men for x
number of days”
So, x = (x – 10) * {y/(4y/5)}
Or, x = (5/4)( x – 10)
Or, 4x = 5x – 50
Or, x = 50 days. answer is a.
If 40 men can make 30 boxes in 20 days,
How many more men are needed to make 60 boxes in 25 days?
a)
28 b)
24 c) 22 d) 26
Answer:
40 x (60/30) x (20/25) =
64 men
So, extra men = 64 – 40 = 24. Answer is b.
Note: for making more number of boxes you will need more
number of men. So fraction must be more than 1............... (60/ 30)
In more number of days you will need less number of men.
So, the fraction should be less than 1............................(20/25)
In a camp, food was sufficient for 2000
people for 54 days. After 15 days, more people came and the food last only for
20 more days. How many people came?
a)
1900 b)
1800 c) 1940 d) 2000
Answer:
We will re-phrase the question
There is food for 2000 people for (54 – 15 = 39) days. Food lasted
for 20 days. So, how many people where there.
= 2000 x (39/20) = 3900
So, extra people who joined was = 3900 – 2000 = 1900
answer is a
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).
Saturday, August 3, 2013
15-chain rule / time and work
If 10 workers can dig a trench 23/4 feet long in one day, then how many workers will be required to dig a trench 23 feet long in 3 days time?
14-chain rule / time and work
For a certain job, 60 days are required
for a group of men. If 8 more are added to the group, then it would take 10
less days to complete the job. How many men were there initially?
13-chain rule / time and work
8 men or 12 boys can do a piece of work
in 50 days. In how many days will 11 boys and 6 men do the job?
12-chain rule / time and work
6 men or 12 boys can do a piece of work
in 40 days. In how many days will 16 boys and 24 men do the job?
11-time and work / chain rule
For a certain job, 40 days are required
for a group of men. If 12 out of the group never turned up for the job, then it
took the remaining men 64 days to get the job completed. How many men were
there initially?
10-chain rule / time and work
A student hostel has 280 students. It has
ration for 20 days. 40 students leave for home on Christmas after 8 days of
staying together. How many days will the ration last?
9- chain rule / time and work
3 men or 5 boys can do a piece of work in
30 days. In how many days will 5 boys and 12 men do the job?
chain rule
In a hostel, ration for 2000 students is
sufficient for 54 days. After 15 days some more people join in and the ration
lasted for only 20 more days. How many people joined in later?
chain rule
48 men working 4 hours a day can complete
the work in 10 days. How many men will be required to complete the work in 6
days, working 10 hours a day?
chain rule / unitary method
40 girls can make 30 boxes in 20 days. How many more girls
should be employed to prepare 60 boxes in 25 days?
Chain rule / unitary method
If 12 books cost Rs 80 what will be the cost of 30 books?
(alternate to unitary method)
Wednesday, July 24, 2013
Arithmetic
If x kg of tea cost $y,
how many $ will y kg of the same tea cost?
Answer:
Cost
of 1 kg tea = y/x
Cost
of y kg tea = (y/x).y = y2/x
Wednesday, July 17, 2013
Barter
A man has bought 6 oxen and 5 cow of $ 17120 and would lose
$160 by exchanging 3 oxen for 5 cows. What is the price of a cow?
Answer:
Exchange: 3 oxen for 5 cows
So, 6 oxen for 10 cows == loss = 160 x 2 = $320
Now, 6 oxen + 5 cow = 10 cow + 5 cow = $17120 – $320 = $16800
Therefore, 15 cow = $ 16800
Or, 1 cow = 16800/15 = $ 1120
If 50 meters of muslin and $ 360 is given in exchange for 36
meters of silk at $30 per meter, then what is the price of muslin?
Answer:
Cost of 36 meters of
silk = $30 x 36 = $ 1080
50 meters of muslin +
$ 360 = $ 1080
Therefore 50 meters of
muslin = $720
So, price of muslin =
$720/50 = $ 14.4
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