Pension

Peter’s wife,Catherine, is employed by Peter’s partnership. She is paid an annual salary of £290,000 in thet ax year 2021/22.She pays10% of her salary in to her employer’s occupational pension scheme and her employer(the partnership) pays a further 5% into the same scheme. Catherine also made a gross contribution into a personal pension scheme in the tax year of £10,000. They jointly own a property and has generated £67000 as profits.
What is Catherine’s Annual Allowance?

In the solution 290000*10% pension is deducted and Catherine’s and employer’s contribution to occupational pension (10%+5%)×£290,000 is added to the adjusted income. Can you please explain why?