A woman has Rs 10,000 with her. She calculated that she could spend Rs x every day on her holidays.

Under the assumption the full amount was exhausted in both cases, your formula is this:
{Days} * {Expenditure per day} = {Total expenditure}
Denote planned days = d.
d * x = 10000
(d + 10) * (x - 50) = 10000
And solve.