Loona  became the subject of too much attention and became quite famous because of her exploits of tiger hunt. Mrs. Packletide did not want to be left behind. She wanted to outshine Loona Bimberton. Hence, she wished to kill a tiger.
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it is not that Mrs. Packletide wanted to kill the tiger She wanted to show that she was no less than Loona Bimberton. and she had thrown a luncheon party in loona's house Hence, she wished to kill a tiger.