Ramesh, Mahesh and Suresh took a house on rent for one year for Rs 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:
Show Hint
For any partnership or sharing of expenses based on time duration, avoid dividing the total rent by the total "man-months" directly unless the problem statement specifies an alternate sharing scheme.
Break down the problem chronologically into intervals of constant occupancy and allocate rent for each period among the active tenants.
This systematic process prevents errors.
Step 1: Understanding the Question:
This is a problem based on the division of expenses (partnership concept).
Three individuals rent a house for a year (12 months), but they do not stay for the same duration.
The total rent must be shared among them in proportion to the time they spent in the house, with the rent for any period being shared equally among those residing there during that time. Step 2: Key Formula or Approach:
The total rent is Rs 14184 for 1 year (12 months).
The monthly rent of the house is:
\[ \text{Monthly Rent} = \frac{\text{Total Rent}}{12} \]
We divide the year into three distinct intervals based on who was occupying the house:
1. First 4 months: Ramesh, Mahesh, and Suresh are living together. Rent is split among 3 people.
2. Next 5 months (months 5 to 9): Ramesh and Suresh are living together (Mahesh has left). Rent is split among 2 people.
3. Remaining 3 months (months 10 to 12): Ramesh is living alone (Suresh has left). Rent is paid fully by Ramesh. Step 3: Detailed Explanation:
• Calculate Rent for Period 1 (First 4 months):
Total rent for these 4 months:
\[ 4 \times 1182 = \text{Rs } 4728 \]
Since all three (Ramesh, Mahesh, and Suresh) lived together, each pays an equal share:
\[ \text{Share of each} = \frac{4728}{3} = \text{Rs } 1576 \]
• Calculate Rent for Period 2 (Next 5 months):
Total rent for these 5 months:
\[ 5 \times 1182 = \text{Rs } 5910 \]
Since only Ramesh and Suresh lived during this period, each pays:
\[ \text{Share of each} = \frac{5910}{2} = \text{Rs } 2955 \]
• Calculate Rent for Period 3 (Last 3 months):
Total rent for these 3 months:
\[ 3 \times 1182 = \text{Rs } 3546 \]
Only Ramesh lived in the house, so he pays the entire amount:
\[ \text{Ramesh's share for Period 3} = \text{Rs } 3546 \]
• Calculate Total Rent Paid by Each Person: • Mahesh (B): He only lived during Period 1.
\[ \text{Rent paid by Mahesh} = \text{Rs } 1576 \]
This matches List-II (I).
• Suresh (C): He lived during Period 1 and Period 2.
\[ \text{Rent paid by Suresh} = 1576 + 2955 = \text{Rs } 4531 \]
This matches List-II (IV).
• Ramesh (A): He lived for all 12 months.
\[ \text{Rent paid by Ramesh} = 1576 + 2955 + 3546 = \text{Rs } 8077 \]
This matches List-II (III).
• Calculate 50% of Total Rent (D):
\[ 50\% \text{ of } 14184 = 0.5 \times 14184 = \text{Rs } 7092 \]
This matches List-II (II). Step 4: Final Answer:
Matching the items:
A $\rightarrow$ III
B $\rightarrow$ I
C $\rightarrow$ IV
D $\rightarrow$ II
This combination corresponds to option (B).
