From the total water absorbed by the root system, how much water does the plant use for transpiration and how much water does the plant use for photosynthesis?
Your question does not have a single answer, and depends on several factors: the type of photosynthesis (C3, C4 or CAM), the species of the plant, temperature, amount of ground water, relative humidity, luminosity etc.
However, as a good guess, I used to say to my students that around 1% of the absorbed water is used in photosynthesis, the remainder (99%) being either lost by transpiration or used for cell growth. Once more, have in mind that this is a rough estimate, the real number varies.
Now let's have a look at more precise figures, from Bieleski et al. (1999):
As you can see, we have here three kinds of plants (C3, C4 and CAM) here. The column you want is TR ratio (which stands for Transpiration/Photosynthesis ratio). If we consider a C3 plant, the number goes from 450 to 600.
Let's take 600 as an extreme example. A TR ratio of 600 means that the plant loses 600g of H2O to fix 1g of CO2, using approx. 0.4g of water (You'll have to do some math here, using photosynthesis equation), but that tell us that the amount of water used for photosynthesis is less than 0.1% of the transpired water.