Aptitude - Chain Rule - Discussion

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.

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.

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.

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

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.

Lets assume 1 kg of food is eaten by each person.

Total quantity of food =150 x 45
= 6750kg.

Quantity of food finished in ten days by 150 men = 150 x 10
= 1500kg.

Amount of food remained = 6750 - 1500.
= 5250kg.

Therefore, number of days the remaining food can be eaten by 125 people
= 5250/125 = 42 days.

25 men left after 10 days.

So, let's assume we save their food for the next 35 days and keep that food aside.
That should be equal to 25 * 35 = 875.
After 45 days we bring that food out.
Now, there are 125 men left in the fort.
So, 125 men will be consuming (food that was not consumed)25 * 5 times the food.
For the each day i.e 875 ÷ 125 = 7.
Hence now total days = 35 + 7 = 42.

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?

@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?

@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.