An extremely old woman

Our grandmother, known as Mim, used to look after Penny (aged 3 or 4) while Mother was teaching.

One day she popped Penny on top of the sideboard to remove her from some mischief. Penny was furious, and hurled her deadliest insult in revenge:

"You're an extremely old woman and you look like one!"

Unfortunately for the effect, Mim thought this was so funny that it became a standing joke. She began to sign family letters as ye anciente Mim, and refer to herself as this extremely old woman.

How old was that extremely old woman at the time, I wonder? In her 50s?