  The compounds Lu$_5$Ir$_4$Si$_{10}$ and Lu$_5$Ir$_4$Ge$_{10}$ crystallize in
the tetragonal Sc$_5$Co$_4$Si$_{10}$ type structure. Lu$_5$Ir$_4$Si$_{10}$ is
known to superconduct below 3.9 K and it also exhibits a strongly coupled
charge density wave (CDW) transition below 83 K. Lu$_5$Ir$_4$Ge$_{10}$
undergoes a transition into the superconducting state below about 2.4 K without
any CDW transition at higher temperatures. Recent Si NMR measurements on
polycrystalline samples of Lu$_5$Ir$_4$Si$_{10}$ suggest that there is no
energy gap at the Si site across the CDW transition. Thus it is of interest to
study the evolution of the superconductivity and the CDW transition when we
dope at the Si site with small quantities of Ge. Here we present the evolution
of T$_C$ and T$_{CDW}$ with concentration x of Ge in the alloy system
Lu$_5$Ir$_4$(Si$_{1-x}$Ge$_x$)$_{10}$ (x=0.0, 0.005, 0.01, 0.02, 0.05, 0.1,
0.2, 0.4, 1.0) as estimated from dc susceptibility measurements. We find that
the CDW is strongly suppressed with increasing x and there is a simultaneous
enhancement of the superconducting transition temperature T$_C$ from 3.9 K for
the undoped sample to almost 6.6 K for only 10% concentration of Ge in the
alloy.
