What is transaction demand for money? How is it related to the value of transactions over a specified period of time?

Money is the most liquid of all assets because a person having money (cash) can convert it into anything he likes. Therefore, demand for money is the demand for liquidity. Broadly there are two main motives for holding money — transaction motive and speculation motive. Accordingly, there are two constituents of demand for money, namely, transaction demand for money and speculation (asset) demand for money as explained below.
(a) Transaction demand for money   Transaction demand for money is the amount of money required for current transactions of individuals and firms. It is the quantity of money that all the individuals and firms desire to keep on hand for purpose of financing their forthcoming expenditure. The main reason to hold money in cash is for meeting day-to-day or routine transactions. In other words, this is done to bridge the interval between receipt of income and expenditure. For instance, a worker who gets his wages on the first day of the month has to spend it continuously throughout the month on purchase of goods and services. The same consideration applies to businessmen. In short, the principal motive for holding cash is to carry out transactions. For simplifying the discussion, we aggregate precautionary demand for money (to provide for emergencies like sickness or accident) with transaction demand. What determines transaction demand for money?
According to Keynes, transaction demand for money is mainly detertmined by the level of income. It is positively associated with the level of income. Higher the level of income, the larger would be the size of money holdings for transactions. For example, the size of transaction demand for money at income level of र 1000 crores will be larger than that at the income level of र 700 crores. Mind, it is not the size of national income but proportion of it which people hold as cash balance that determines the transaction demand for money. It is perfectly interest inelastic.
(b) Relationship between transaction demand for money and value of transactions. The transaction demand for money of the economy is fraction of total value (volume) of transactions over a unit period of time. Symbolically:

It shows that transaction demand for money  is a positive fraction (K) of total value of transactions (T). This can be clarified with a simple example of two-person economy consisting of one person firm and the other person a worker. Suppose the worker gets a salary of र 1000 on first day of every month and spends over the month his entire income on goods and services produced by the firm. His monthly cash balance at the beginning of the month is र 1000 and at the end of the month is Rs 0. As against it, the firm has Rs 0 balance at the beginning of the month and र 1000 at the end of the month through its sales to the worker. Average money holding of worker is र 500  and of the firm is also र 500  Clearly whereas transaction demand for money is र 1000 (= 500 by the worker + 500 by the firm), total volume of monthly transactions in the economy is र 2000 as the firm has sold its goods and services worth र 1000 to the worker and the worker has sold his services worth र 1000 to the firm. Hence the transaction demand for money is a fraction (here 50%) of total volume of transactions over a unit period of time.