Ajay, Sunil, Krishna and Sumit are good friends. They rent a house together at ₹15,000 per month. Ajay lives in this house for only 15 days in a month. Krishna and Sumit are also working and they decide to jointly contribute ₹10,000 as their share of the rent. Sunil lives in the house for the whole month. If Ajay and Sunil decide to contribute to the rent based on the number of days they live in the house, what would be the share of rent paid by Ajay, Sunil, Sumit and Krishna respectively?

Correct option is B

Given:

Total rent for the house = ₹15,000 per month

Ajay stays for 15 days

Sunil stays for the whole month (30 days)

Krishna and Sumit contribute ₹10,000 together for their share.

The rent will be shared based on the number of days each person stays in the house.

Concept Used:

To calculate each person's share of rent, we need to consider:

Ajay and Sunil's rent contribution will be proportional to the number of days they stay.

Solution:

Let the total number of days the house is occupied in the month be:

Total days=30 (for Sunil)+15 (for Ajay)=45 days

Ajay and Sunil's rent contribution is based on the number of days they stay,

and they will contribute the remaining ₹5,000 (since Krishna and Sumit already contribute ₹10,000).

Thus, we calculate their share based on their respective days.

Krishna and Sumit's contribution:
They contribute ₹10,000 together, so each of them contributes:

​$$\text{Krishna's share} = \frac{10,000}{2} = ₹5,000 \quad \text{and} \quad \text{Sumit's share} = ₹5,000$$​

Ajay and Sunil's contribution:
The remaining rent to be shared between Ajay and Sunil is:

Remaining rent=₹15,000−₹10,000=₹5,000

Ajay's share:
Ajay stays for 15 days, so the total days between Ajay and Sunil is 45 days. Ajay's share of the total days is:

​$$\text{Ajay's fraction} = \frac{15}{45} = \frac{1}{3}$$​

Thus, Ajay's share of the remaining rent is:

​$$\text{Ajay's rent} = \frac{1}{3} \times 5,000 = ₹1,666.67$$​

Sunil's share:
Sunil stays for the whole month (30 days), so Sunil's fraction of the total days is:

​$$\text{Sunil's fraction} = \frac{30}{45} = \frac{2}{3}$$​

Thus, Sunil's share of the remaining rent is:

​$$\text{Sunil's rent} = \frac{2}{3} \times 5,000 = ₹3,333.33$$

Share of rent paid by Ajay, Sunil, Sumit and Krishna=$$\frac{1}{3} \times \frac{5,000}{15000}$$ , $$\frac{2}{3} \times \frac{5,000}{15000}$$ , $$\frac{5000}{15000},\frac{5000}{15000}$$​

=$$\frac{1}{9},\frac{2}{9},\frac{1}{3},\frac{1}{3}$$​​