Lake inflow-outflow problem The evaporation from a lake is to be calculated by the water balance method.   Inflow to the lake occurs through three small rivers, A, B and C.   The outflow occurs through the river D.   Calculate the evaporation from the lake surface during summer (May – August) if the water level was +571.04 m on May 1 and +571.10 m on August 31.   The lake surface area is 100 km$^2$.   The precipitation P during the period was 100 mm. Average inflows and outflow are given below:          

              River      Catchment(km2) Average Q(m3/s)
                A             150        15
                B             120        20
                C             130        17
                D                        45


This is the way I have attempted it:


Total Inflow ( by A, B, C) $= 52\ \mathrm{m^3/s}$.
Outflow (by D, assuming that D is fed by the lake) $= 45\ \mathrm{m^3/s}$.
Inflow - Outflow = Change in storage (which is in turn change in elevation × area)
Net Inflow into the lake = Inflow by 3 rivers + Precipitation
$$                           
= (52\ \mathrm{m^{3}/s} \times 122 \times (30\ \mathrm{days}+31+30+31)\times24\times60\times60 + 0.1\ \mathrm{m}\times100\times10^3 \mathrm{m}^2)
$$
Total Outflow = Outflow + Evaporation
$$
                = (45\times122\times24\times60\times60 + E),
$$
where E is the component to be found.
Change in storage = Change in elevation × Area
$$
                  = (571.10 - 571.04)\times100 \times 10^6 E = 0.68\ \mathrm{m}
$$
Everything you did looks reasonable.  There is one error in the 'net inflow into lake' line where you take the area of the lake to be $100\cdot10^3\ \text{m}^2$ instead of $100\cdot10^6\ \text{m}^2$, but that might just be a typo.  

In general, this type of problem is much easier to work (especially when you think you've made an error) by keeping everything symbolic.  For your problem I would define the variables


$i$: inflow into the river in $\frac{\text{m}^3}{\text{s}}$
$o$: outflow from the river in $\frac{\text{m}^3}{\text{s}}$
$r$: inflow from rain in $\text{m}$
$e$: evaporation in $\text{m}^3$
$\Delta h$: change in height of the lake in $\text{m}$
$A$: area of the lake in $\text{m}^2$
$\Delta t$: time period in $\text{s}$


The equilibrium equation is then 

$$\text{sum of inflows}-\text{sum of outflows}=\text{change in storage}$$

which is written in terms of the defined variables as

$$i\ \Delta t+r\ A-o\ \Delta t-e=\Delta h\ A.$$

You can check that this equation at least makes sense in terms of units by observing that all of the terms have units of volume, i.e. $\text{m}^3$.  Finally, you can rearrange the equation to solve for the variable of interest;

$$e=(i-o)\Delta t+(r-\Delta h)A.$$

At this point you can plug in the numbers.