Rent and change of tenant

Tenancy Types and Management

Hi, I have two important questions

1) I have 3 tenants sharing a 3-bed maisonette. They are on 1 contract. One of the tenants wanted to leave and I agreed this as long as she found a replacement. Unfortunately the new person dropped out on the day he was supposed to move in. They have found another person but 2 weeks too late for the monthly rent. Who is responsible for the outstanding rent (2 weeks)??? The contract they signed states the full monthly rental - not individual amounts.

2) When this new person moves in, can I get them to sign a copy of the contract just with amended dates or do I make it an amendment to the original contract? What is the legal course of action?

I would be very grateful for any advice.