Question

The expenses of a hostel are partly constant and partly varying with the number of occupants. If there are 20 occupants, then each of the occupants has to bear 650 per month and if there are 5 more occupants, then the share of each of the occupants comes down by 50 per month. How many occupants
would be there if the share of each occupant is 500?
(A) 35 (B) 40 (C) 45 (D) 50​

Answer 1

(A) 35

The number of occupants  would be there if the share of each occupant is 500 = 35.

Step-by-step explanation:

Given : The expenses of a hostel are partly constant and partly varying with the number of occupants .

If there are  20 occupants, then amount each occupants has to bear per month = Rs 650

Let x be the number of times 5 more occupants added and y be the total number of occupants

If there are 5 more occupants, then the share of each of the occupants comes down by Rs 50 per month.

$y=20+5x$   (1)

To make the share Rs 500 per month,  the equation we get

$650-50x=500$

we first subtract 500 and add 50 xfrom both sides , we get

, we get $50x=150\Rightarrow\ x=\dfrac{150}{50}=3$

i.e. we need to add 3 times 5 more occupants to make the share Rs 500.

i.e. The total occupant would require : y= 20+3(5)=20+15=35    (From (1))

Therefore , the number of occupants  would be there if the share of each occupant is 500 is 35.

# Learn more :

The expense of a lunch are partly constant and partly proportional to the number of guests .The expenses amount t rs.750 for 7 guest and rs.970 for 11 guests, then find the expense for 17 guests.

a)1450 b)1550 c)1650 d)1750

https://brainly.in/question/11428063

Answer 2

Answer:

50

Step-by-step explanation:

Do not use the direct ratio method. Options are very tricky. Here our initial answer might look like it is 35 but it 50. I shall explain how.

Make sure you form correct equations.

Total expense = X + y which are variables.

Equation one will be :

Total expense (650*20=13,000)

X+20y=13,000

Similarly, equation 2 will be,

X+25y=15,000

Equation 2-1 will give you:

5y=2000

So we get the value of y as 2000/5 which is 400.

Substituting the value of y in equation one, we get the value of x.

X= 13,000-8000=5000

Let the number of occupants be N for the answer we need.

N occupants share Rupees 500 each.

So the equation will be:

500N=X+Ny

Substituting the values of X and y here we get the value of N.

500N - 400N = 5000

100N = 5000

N = 5000/100 = 50.

The number of occupants when the share of each is Rupees 500 is 50.

Hope this helps you. Even I thought it was 35 and was corrected. Cheers!