Let the total amount invested =M
At the end of the year the investment was worth =1.1M
1.1M - M =0.10M - profit made
She spent 20% on tennis racket, which means she still had 80% left.
0.8 *0.10M =0.08M left
She spent 1/8 on tennis outfit, which means she still had 7/8 left.
7/8 * 0.08M =0.07M left
0.07M =140, solve for M
M =140 /0.07
M =2,000 Euros - initial amount invested.