A question is given, followed by three statements labelled I, II and III. Identify which of the statements is/are sufficient to answer the question.

Question:

What is the total expense when the hostel has 189 occupants?

Statements: Total expenses of the hostel consist of two parts: one varies directly with the number of occupants and the other is fixed.

I. When it had 150 occupants, its total expense was ₹79,500.

II. When it had 240 occupants, its total expense was ₹1,15,500.

III. When it had 200 occupants, its total expense was ₹99,000.

Correct option is D

Given:

The total expense of the hostel consists of:

• A fixed part (F)
• A variable part that increases directly with the number of occupants (k × number of occupants)

So,
Total Expense = F + k × Number of Occupants

Solution:

Using the Statements:

We’ll now create equations from the statements based on the format above.

Statement I:
When there were 150 occupants, total expense = ₹79,500
So,
F + 150k = 79500 → Equation (1)

Statement II:
When there were 240 occupants, total expense = ₹1,15,500
So,
F + 240k = 115500 → Equation (2)

Statement III:
When there were 200 occupants, total expense = ₹99,000
So,
F + 200k = 99000 → Equation (3)

Check sufficiency:

Using Statements I and II:

Subtract Equation (1) from Equation (2):

(240k - 150k) = 115500 - 79500
90k = 36000 → k = 400

Now substitute back into Equation (1):
F + 150×400 = 79500 → F + 60000 = 79500 → F = 19500

Now we can calculate the expense when occupants = 189:
Expense = F + 189×k = 19500 + 189×400 = 19500 + 75600 = ₹95,100

So, Statements I and II are sufficient

Using Statements I and III:

Subtract Equation (1) from Equation (3):

(200k - 150k) = 99000 - 79500
50k = 19500 → k = 390

Now substitute back into Equation (1):
F + 150×390 = 79500 → F + 58500 = 79500 → F = 21000

Now for 189 occupants:
Expense = F + 189×k = 21000 + 189×390 = 21000 + 73710 = ₹94,710

So, Statements I and III are also sufficient

Conclusion:

• Any two of these statements involving Statement I are enough to solve the question.
• So, the correct answer is:

Option (D) – I and II or I and III