We present X-ray fluorescence observations of the lunar surface, made by the Chandrayaan-1 X-ray Spectrometer during two solar flare events early in the mission (12th December 2008 and 10th January 2009). Modelling of the X-ray spectra with an abundance algorithm allows quantitative estimates of the MgO/SiO2 and Al2O3/SiO2 ratios to be made for the two regions, which are in mainly basaltic areas of the lunar nearside. One of these ground tracks includes the Apollo 14 landing site on the Fra Mauro Formation. Within the 1σ errors provided, the results are inside the range of basaltic samples from the Apollo and Luna collections. The Apollo 14 soil composition is in agreement with the results from the January flare at the 1σ uncertainty level. Discrepancies are observed between our results and compositions derived for the same areas by the Lunar Prospector gamma-ray spectrometer; some possible reasons for this are discussed.