Ajay, Sunil, Krishna and Sumit are good friends. They rent a house together at Rs. 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 Rs. 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?

Option 3 : \(\frac{1}{9}, \frac{2}{9}, \frac{1}{3}, \frac{1}{3}\)

Given:

Rent of the house = Rs.15000 per month 

Share of rent contributed jointly by Krishna and Sumit = Rs.10000

No of days spent by Ajay = 15 days per month 

No of days spent by Sunil = 30 days or Whole month 

Calculation:

Fraction of rent to be paid equally by Sumit and Krishna over total rent = Rs.10000/Rs.15000 = 2/3 

⇒ Sumit : Krishna = 1/3 : 1/3 ......(1)

Fraction of rent to be paid by Ajay and Sunil over total rent = Rs.5000/Rs.15000 = 1/3

Ratio of days spent by Ajay and Sunil = 15 days : 30 days = 1 : 2 

Further, Ajay and Sunil will share their rent on the basis of days spent by them per month, ratio will be (Days spent × Share of rent): 

⇒ Ajay : Sunil = 1/3 × 1/3 : 1/3 × 2/3 

⇒ 1/9 : 2/9 .....(2) 

∴ By (1) and (2), the share of rent paid by Ajay, Sunil, Sumit and Krishna will be:

⇒ 1/9 : 2/9 : 1/3 : 1/3