Aptitude - Chain Rule - Discussion

Discussion :: Chain Rule - General Questions (Q.No.4)

4. 

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 1
5
[B].
37 1
4
[C]. 42
[D]. 54

Answer: Option C

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.


Suresh Kumar said: (Aug 21, 2010)  
Hi,

I always confused to solve these type of problems. Please help me, how to solve these type of problems in very efficient way.

Vishu said: (Sep 17, 2010)  
Why it is given?

After 10 days : 150 men had food for 35 days.

Rahul said: (Oct 28, 2010)  
If 150 men have food for 45 days then after 10 days they have food for only 35 days left. That is what is given. So the problem now is:
150 men food for 35 days, 125 men food for how much? 150/125 = 6/5 so 6/5 x 35 = 42 days.

Vikas said: (Nov 29, 2010)  
Hi All,

I was little puzzled the way they have solved the question. I hv been average students so high funda I cant understand. Simple and natural way to do it is as follows:

Total food available=150*45
They all consume food for 10 days, food consumed in 10 days=150*10
Food left after 10 days=150*45-150*10
For how many days 125 people can eat this food=
(150*45-150*10)/125
=42

I hope that was simple to understand

Uttam said: (Feb 5, 2011)  
No. of men =>(1/no of days), that is inversely proportional.

We can write,

m=>1/d

So,

(150/125)=(x/35)

x=42 days.

Hari said: (Feb 21, 2011)  
@Vikas.

Nice way of explanation.

Bandita said: (Mar 11, 2011)  
@ Vikas its excellent.

Lokesh said: (Mar 16, 2011)  
Vikas you are great

Asha said: (May 17, 2011)  
@vikas. Thanks. Good Explanation.

Vishnu said: (Aug 4, 2011)  
@vikas.Good Explanation.thanks alot

Sabyasachi Samal said: (Aug 18, 2011)  
Thanks i get it right now.As indirect proportion we can usethe less no of people more number of days.
so put 125/250 so first put the less number of people then the more number of people.

Neha Garg said: (Sep 12, 2011)  
@Vikas thanks.

Saleh said: (Oct 29, 2011)  
Thanks vikas. But any one help - How find out direct and in direct proportion?

Ajay Kumar said: (Dec 1, 2011)  
Vikas's method is excellent.

Yogendra said: (Dec 20, 2011)  
Hi, saleh in direct proportion we compare ist to last value &in indirect proportion we take last to 1st Ex-less men,more days(indirect prop.) 125:150

Sugan said: (Dec 28, 2011)  
Great rahul your very right.

Sita said: (Jan 21, 2012)  
@vikas

Nice way of explaining.

Nithin said: (Feb 4, 2012)  
@rahul after 10 days 25 men will leave, so how come we can take as 150? we must take it as 125 right!

Vabs said: (Feb 28, 2012)  
@ vikas

Nice technique

Sakthi said: (Mar 11, 2012)  
Very good explain vikas. Thank you.

Ekta said: (Aug 20, 2012)  
Good explation vikas. Thanks.

Durga said: (Aug 30, 2013)  
There are 150 men and they have food for 45 days.

So available food = 150*45 = 6750.

After 10 days 25 men left.

So food consumed for 10 days 150*10 = 1500.

Now avail food = 6750-1500 = 5250.

Avail food = 5250 and there are 125 men.

So this food avail for = 5250/125 = 42 days.

Tushar said: (Oct 19, 2013)  
HI,

I am always confused to solve time and work questions, so please help me to solve this problem in easy way.

Mandeep Kaur said: (Jun 13, 2014)  
(150*45-150*10)/125.

After solving this we get answer is negative. That is not exist.

Kalyani said: (Jul 31, 2014)  
Thank you @Vikas.

In the first way mentioned example. Why they are considering 150 men food for 35 days. I mean, for only 10 days 150 men will have food. So after that only, remaining 125 men will have food for 35 days na. Clarify my doubt.

Bbc said: (Aug 31, 2014)  
It means that for 35 days 150 men have enough food.
So 25 leave.

Now the question is how many days will the remaining food be enough for 125 men.

Shubham said: (Jan 9, 2015)  
How can you say that total food available is 150*45?

It can be a multiple of 150*45 also.

Let the total amount of food available be x (for 150 men, for 45 days).

Therefore food available for 150 men per day = x/45.

Food available per man per day = (x/45)/150.

Can someone tell me what is the problem in this approach?

Sukumar Satyen said: (Apr 15, 2015)  
Solution step by step:

45 days ---> 150 men ---> 1 food.

1 day ---> 150*45 men ----> 1 food.....equation(1).

10 days ---> (150*45)/10 men ---> 1 food.

10 days ---> 1 man ---> 10/(150*45) food.

10 days ---> 150 men ---> 10/45 food.

Remaining food 1 - 10/45 = 35/45 food.

From equation (1),

1 food ---> 150*45 men ----> 1 day.

1 food ---> 1 man ----> 150*45 days.

35/45 food ---> 1 man ----> 35*150 days.

Remaining men after 10 days = 150-25 = 125 men.

35/45 food ---> 125 men ----> 35*150/125 days = 35*6/5 = 42 days.

Vatageve said: (Jul 11, 2015)  
(150*45) = (10*150)+(125*y).

So y = 42.

Vatageve said: (Jul 11, 2015)  
In the start, total food (150*45).

1-10 days used food (10*150).

After 10 days remaining food (125*y).

So (150*45) = (150*10) + (125*y).

y = 42.

Manisha said: (Jul 21, 2015)  
I can't understand to this example please can you explain how to solve this example?

Nitish Guleria said: (Aug 31, 2015)  
@Manisha.

Don't be confused question mean in 1 day 150 men eat a food. So in 45 days total food they eat are 45*150 = 6750.

Okay now in 10 days 150 men eat food = 1500 okay now remaining food = 5250 which will be eaten by 125 men in how much days then answer are 5250/125 = 42 days.

Jagan said: (Jun 11, 2016)  
@Vikas.

Your explanation clear and easy to understand. Thank you.

Pooja said: (Jul 21, 2016)  
Wow! Great explanation @Vikas.

Rohit said: (Jul 28, 2016)  
Nice explanation @Sukumar.

Giri said: (Aug 9, 2016)  
Vikas, simply well explained. Thanks.

Hemant said: (Jan 4, 2017)  
The question is based on proportion.
If a and b are in direct proportion ,
a = k x b, where k is constant of proportionality.
a/b =k ,

If a and b are in inverse proportion,

a =K/b

a x b = k.

Now in our given question.

150 men, .food available for 45 days.
After 10 days,
For 150 men food available for 35 days.

More no.of men less no of Days

The relation is inverse.

Therefore, 150 x 35= constant.

Now 25 left.

Men are 125, no. Of days = x.

125 * X = constant (* means multiplication).

150 x 35 = 125*X
150 X 35
---------------- =X
125

X= 42.

NO. OF DAYS THE REMAINING FOOD WILL LAST FOR 125 men is 42.

Shreya said: (Jan 6, 2017)  
Very good explanations. Thank you all.

Shreya said: (Jan 6, 2017)  
Very good explanations. Thank you all.

Ravi said: (Jan 12, 2017)  
Thank you for the best explanations @Vikash & @Nitish.

Ma Haque said: (May 8, 2017)  
Good explanations. Thank you all.

Liza Bhattarai said: (Jun 28, 2017)  
Hi please solve my question.

In a hostel, 150 students have provision for 45 days. For how many days will provision last for 125 students?

Siddharth said: (Jun 29, 2017)  
@Liza.

1 student has provision for 150 x 45 days.
125 students have provision for 150 x 45 / 125 = 54 days.

Lekshmi said: (Jul 7, 2017)  
Great explanation, Thanks @Vikas.

Puspak said: (Jul 18, 2017)  
In a camp of 2200 men their stock of food for 50 days. Some men came after 17 days and remaining food lasted for 20 days more. How many men came after 17 days?

Please solve this.

Star said: (Jul 19, 2017)  
What if the question had been how many more days the food lasts? Then would the answer be 42-35 = 7 more days.

Star said: (Jul 19, 2017)  
@Pushpak.

I guess 1430 men came after 17 days,
2200*33 = (2200+x) * 20.

Manisha Sinha said: (Jul 24, 2017)  
@Pushpak.

The answer is 1430.

Niranjana said: (Sep 6, 2017)  
@Vikas.

Could you explain this sum for me, please. In a fort, there was sufficient food for 24 weeks for 200 soldiers. 80 more soldiers join the group at the end of one week and quantity of food served to each soldier was reduced from 900 gm to 750 gm. For how many days the rest food would last now?

Divya G said: (Sep 27, 2017)  
Can anyone help me to give clear answer for this?

Sameenamhd said: (Oct 24, 2017)  
If 9 mens are at work and they food for only 26days. If 4 people are joining the work then in how many days the food will complete? Can anyone answer this?

Mugdha said: (Nov 12, 2017)  
My que is that if x men consume x kg of food in x days, then why men will consume why kg of food in ? how many days?

Anshika said: (Dec 1, 2017)  
Let the total food be x.

150 men ate x food for 45 days i.e. 150 men ate x food for first 10 days and rest 35 days

But when 25 men left after 10 days the food left was only what 150 men would eat for the rest 35 days as mentioned above.

Hence 125 men only had food that 150 men would have eaten for rest 35 days.

Thus,
150:125= days:35 ( inversely proportionate)
Days = 150*35/125=42.

Anshika said: (Dec 1, 2017)  
@Sameenamhd.

Your question is an inversely proportionate one without any condition.

If 9 people eat for 26 days.
Then 13(9+4) will eat for x.
9:13=x:26 then x=18 days.

Manish said: (Dec 21, 2017)  
25 persons food remain for next 35 days.
125 person can eat the above food fro next 7 days.

ie 25*35/125=7.
so 35 days + 7 days=42 days.

Kaustav Roy said: (Dec 28, 2017)  
In this kind of problems always consider.

Amount of food= no. of days * no. of men.
Food amount will always be constant, hence equate the conditions accordingly.

Firstly,

Amount of food = 150 * 45
After 10 days, amount of food = 150*10
Amount of food left after 10 days = 150*(45-10) = 150 * 35
This food amount will be consumed by 150-25 = 125 men in 'x' days say,
So,

150*35 = 125*x,
x = 150 * 35/ 125,
x = 42 days.

I hope this solution would make problems of this type easier to solve.

Chhotu said: (Mar 10, 2018)  
Thanks @Vikash.

Shubham Sakhare said: (Mar 23, 2018)  
Let the required number of days be 'x'.
150*45=(150*10)+(125*x),
Hence, x=42.

Aryan said: (Jun 22, 2018)  
A ship has food provision for 300 people for 30 days. If 200 more people join the ship, how long will the provisional last?

Can anyone solve this?

Shashi said: (Aug 17, 2018)  
@Durga.

Thanks for the explanation.

Sourav said: (Oct 25, 2018)  
Thanks @Vikas.

Ram said: (Nov 23, 2018)  
Thanks @Vikas.

B.Saimanasa said: (Apr 5, 2019)  
Why can't the equation be 125 * 150 = 45 * x?

Harish said: (Aug 3, 2019)  
If men decrease then no of days food last will increases for eg: men is halved then days will be doubled.

Similarly, 125 is 5/6th of 150.
So 6/5th of 35 is 42 days.

Harish said: (Aug 3, 2019)  
@Aryan.

A ship has food provision for 300 people for 30 days. If 200 more people join the ship, how long will the provisional last?

For 100 people 90 days.
For 500 people 90/5=18 days.

Lokesh Soni said: (Sep 13, 2019)  
150 men have food for 45 days.
150 x 45 = 6765.

After 10 days the food we have 45-10=35
35x150 = 5250.

Men left after 10 days = 25 means we have 125 men
6765-5250/125 = 48.

Paawan said: (Nov 11, 2019)  
12 workers earn 2128 rs but wrking 7 hours per day for 10 days. 18 workers can earb how much amount by working for 15 days 5 hrs per day?

Gaurav said: (Nov 20, 2019)  
Not Rahul, Vikas has a good explanation.

Vineetha said: (Apr 8, 2020)  
Thanks @Vikas.

Akash said: (Jul 19, 2020)  
Thanks for explaining @Vikas.

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