A hostel had provisions for 250 men for 40 days. If 50 men left the hostel, how long will the food last at the same rate?

Let the remaining food will last for D days.
500 men had provisions for (27 ? 3) = 24 days.
( 500 + 300 ) men had provisions for D days.
More men, Less days ( Indirect Proportion )
we can write as :-
? 800 : 500 :: 24 : x ? (800 × D ) =( 500 × 24 )
? ( 500 × 24 ) /800 =15
Therefore , 15 days is correct answer .

Given in the question,
Let y be the persons there originally .
Work done by y persons can finish = 100 days
If there were 10 persons less, it would take more days finish the work in 10 days
i.e. ( y - 10 ) = 110
According to question ,
y × 100 = ( y - 10 ) × 110
? 100y = 110y - 1100 ? 10y = 1100 ? y = 110
Therefore , 110 persons were there originally .

As per given question,
8 persons can build a wall 140 meter long in 42 days.
1 persons can build a wall 140 meter long in 42 x 8 days.
1 persons can build a wall 1 meter long in 42 x 8 / 140 days.
30 persons can build a wall 1 meter long in 42 x 8 / 30 x 140 days.
30 persons can build a wall 100 meter long in 42 x 8 x 100 / 30 x 140 days.
30 persons can build a wall 100 meter long in 42 x 8 / 3 x 14 days.
30 persons can build a wall 100 meter long in 42 x 8 / 42 days.
30 persons can build a wall 100 meter long in 8 days.

0.6 cm represents 6.6 km in a scale.
1 cm represents 6.6 / 0.6 km in a scale.
80.5 cm represents 6.6 x 80.5 / 0.6 km in a scale.
80.5 cm represents 11 x 80.5 km in a scale.
80.5 cm represents 885.5 km in a scale.

As we know that,
1 Dozen = 12 piece
49 Dozen = 49 x 12 piece
Price of 357 apples is Rs. 1517.25.
Price of 1 apples is Rs. 1517.25 / 357.
Price of 49 x 12 apples is Rs. 1517.25 x 49 x 12 / 357.
Price of 49 x 12 apples is Rs. 1517.25 x 7 x 12 / 51.
Price of 49 x 12 apples is Rs. 1517.25 x 7 x 4 / 17.
Price of 49 x 12 apples is Rs. 2499.
So Price will be around 2500 and answer will be 2500.

According to question ,
3 pumps working in 2 days = 8 × 2 = 16 hours
It means that they can empty a tank in 16 hours .
3 pumps 1 hour work = 1/16
1 pumps 1 hour work = 1/( 3 × 16 )
4 pumps 1 hour work =4 × 1/( 3 × 16 ) = 1 / 12
Hence , they will empty the tank in 12 hours .

Let us assume that each soldier eats one unit of food per day. Thus, total units of food at the beginning will be 1000 x 30 = 30000.
After 10 days 1000 soldiers would have eaten 1000 x 10 = 10000 units of food. Thus food left after 10 days equals 20000 units. Now, there are total of 2000 soldiers who eat one unit of food every day. So, the number of days that 20000 units of food will serve 2000 soldiers is 20000/2000 = 10

Let man's 1 day's work = 1/m
and boy's 1 day's work = 1/n
1 day's work man and boy = 1/24
Man's 6 day's work = 6/m
Now, for 20 days, both man and boy do the work and for last 6 days, only man does the work.
According to the question,
1/m + 1/n = 1/24
? 20(1/m + 1/n) + 6/m = 1
? 20 x (1/24) + 6/m = 1
? 6/m = (1 - 20/24) = 4/24 = 1/6
? 1/n = 1/36
Now from eq. (i)
1/m + 1/n = 1/24
1/36 + 1/n = 1/24
? 1/n = (1/24) - (1/36) = 1/72
Hence, the boy alone can do the work in 72 days.

Let 15 men work for m days.
Work done in 1 days = m/20
Remaining work = (1 - m/20)
25 men's 1 days work = 1/20
1 man's 1 days work = (1/20) x (1/25) = 1/500
10 men's 1 days work = 10/500 = 1/50
10 men's 75/2 days work = (1/50) x (75/2) = 75/100 = 3/4
? (1 - m/20) = 3/4
? m/20 = 1/4
? m = (1/4) x 20 = 5
Clearly, 15 men leave after 5 days.