Ramesh, Mahesh and Suresh took a house on rent for one year for ₹ 14184. They remained together for 4 months and then Mahesh left the house. After 5 more months, Suresh also left the house. Match List - I with List - II. Choose the correct answer from the options given below :List - I (Person) List - II (Rent (in ₹)) A. Rent paid by Ramesh I. 1576 B. Rent paid by Mahesh II. 7092 C. Rent paid by Suresh III. 8077 D. $50\%$ of total rent paid by all three IV. 4531
Understanding the Rent Distribution
The total rent for the house for one year is ₹ 14184. This means the monthly rent is calculated as:
Monthly Rent = $ \frac{₹ 14184}{12 \text{ months}} = ₹ 1182 $ per month.
The problem describes three distinct periods based on who occupied the house:
- Period 1: First 4 months (Ramesh, Mahesh, and Suresh were together).
- Period 2: The next 5 months (Mahesh left, Ramesh and Suresh remained).
- Period 3: The last 3 months of the year (Suresh also left, only Ramesh remained).
Calculating Individual Rent Shares
The rent is distributed based on these periods and the number of people present.
Period 1: First 4 months
During these 4 months, all three shared the house. The monthly rent of ₹ 1182 was divided equally among them.
- Rent per person per month = $ \frac{₹ 1182}{3} = ₹ 394 $.
- Total rent paid by each (Ramesh, Mahesh, Suresh) in this period = $ 4 \text{ months} \times ₹ 394/\text{month} = ₹ 1576 $.
Period 2: Next 5 months
Mahesh left. The rent for these 5 months was ₹ $ 5 \times 1182 = ₹ 5910 $. This amount was split equally between Ramesh and Suresh.
- Rent per person (Ramesh, Suresh) for this phase = $ \frac{₹ 5910}{2} = ₹ 2955 $.
Period 3: Last 3 months
Suresh also left. Ramesh was alone in the house. The rent for these 3 months was ₹ $ 3 \times 1182 = ₹ 3546 $. Ramesh paid the entire amount.
- Ramesh's rent for this phase = ₹ 3546.
Total Rent Paid by Each Person:
- Ramesh's Total Rent: ₹ 1576 (Period 1) + ₹ 2955 (Period 2) + ₹ 3546 (Period 3) = ₹ 8077.
- Mahesh's Total Rent: ₹ 1576 (Period 1 only) = ₹ 1576.
- Suresh's Total Rent: ₹ 1576 (Period 1) + ₹ 2955 (Period 2) = ₹ 4531.
The sum of their rents is ₹ $ 8077 + ₹ 1576 + ₹ 4531 = ₹ 14184 $, which matches the total rent.
Calculating 50% of Total Rent
50% of the total rent is:
$ 0.50 \times ₹ 14184 = ₹ 7092 $.
Matching List - I with List - II
Based on the calculations:
- A. Rent paid by Ramesh = ₹ 8077 (Matches List-II item III).
- B. Rent paid by Mahesh = ₹ 1576 (Matches List-II item I).
- C. Rent paid by Suresh = ₹ 4531 (Matches List-II item IV).
- D. 50% of total rent = ₹ 7092 (Matches List-II item II).
Therefore, the correct matching is A-III, B-I, C-IV, D-II.
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