Budget Preparation

Hi sir

A company has a two-month receivables cycle. It receives in cash 45% of the total gross sales value in the month of invoicing. Irrecoverable debts are 20% of total gross sales value and there is a 10% discount for settling accounts within 30 days.
What proportion of the first month’s sales will be received as cash in the second month?

solution:
consider sales of 100$.

cash receipt in month of sale = 45%*100= 45$
This is after a discount of 10%, so must represent 45/0.9=50 of sales value….. (I am stopping here because my question is regarding this calculation)

2) pears make gross sales of $40,000 per month, of which 10% are for cash, the rest on
credit.
Experience shows that the credit sales are received as follows:
Receivables paying
within one month 40%
within two months 50%
Settlement discounts (for payment within one month) 4%
What will be the total expected cash receipts in any month?

solution:

cash sales 10% of 40,000$
Receivables
36,000$ X 40%X96% – 13,824

My question is about the calculation of settlement discount ..seems both examples are similar but calculated differently… For example in the first example I did also like this “This is after a discount of 10%, so must represent 45/0.9=50 of sales value” …. but in a second example I did exactly the same (36000*40%/0.96) and I got the wrong answer and I don’t understand why… Can you explain why is that?

thanks in advance