A light horizontal lighting boom above a stage turns about a pivot. It balances with a spotlight hanging 0.30 m to the right of the pivot and a counterweight hanging 0.60 m to the left of the pivot. The pivot is then shifted along the boom, but the spotlight and the counterweight stay attached at the same points on the boom. After the shift, the boom balances when the counterweight is replaced by one whose weight is two-thirds of the original counterweight's weight. How was the pivot shifted?
0.10 m0.10\ \mathrm{m}0.10 m closer to the spotlight
0.075 m0.075\ \mathrm{m}0.075 m closer to the counterweight
0.075 m0.075\ \mathrm{m}0.075 m closer to the spotlight
0.10 m0.10\ \mathrm{m}0.10 m closer to the counterweight