The contract in which the contractor needs to complete the work within a fixed sum and fixed time, irrespective of the qualities of different items, is: 

Explanation:

Lump sum contract

• Definition: In a lump sum contract, the contractor agrees to complete the work for a fixed total price within a specified time, regardless of the actual quantities or qualities of the work involved.

• The contract specifies the overall cost for completing the entire project, and the contractor assumes the risk of completing the work within the agreed sum and timeframe.
• It is commonly used for projects with well-defined scopes, where the contractor's risk is higher, but the cost and time are fixed upfront.

Additional Information

Fixed contract

• This is a general term and may refer to a contract where the price is fixed, but it doesn't necessarily imply a fixed sum for the entire project as in a lump sum contract.

Item rate contract

• In an item rate contract, the contractor is paid according to the actual quantities of work done, based on predefined unit rates for each item of work. The total cost is not fixed but is determined by the quantities and rates.

Schedule contract

• A schedule contract lists the detailed description of materials, quantities, and rates for the work to be done. It is similar to the item rate contract but is more detailed in specifying the work schedule and cost breakdown.