Agnes's net salary is S. She spends 1/10 of her salary on rent. She uses 1/2 of the remaining salary for a down payment on a plot. The rest of her salary is spent on giving her mother sh. 2500, shoppi

Let Agnes's net salary be $S$.

Rent = $\frac{1}{10}$ of $S = \frac{1}{10}S$.

Remaining amount after rent = $S - \frac{1}{10}S = \frac{9}{10}S$.

The down payment was $\frac{1}{2}$ of the remaining amount.
Down payment = $\frac{1}{2} \times \left(\frac{9}{10}S\right) = \frac{9}{20}S$.

Amount remaining after down payment = $\frac{9}{10}S - \frac{9}{20}S = \frac{18}{20}S - \frac{9}{20}S = \frac{9}{20}S$.

The amount remaining after the down payment was used for:

• Giving mother: sh. 2500
• Shopping: sh. 7500
• Savings: sh. 12,500 The sum of these amounts equals the amount remaining after the down payment.

Agnes's net salary is sh. 50,000.

Down payment = $\frac{9}{20}S$

The down payment Agnes made was sh. 22,500.

The final answer is $\text{sh. 22,500}$.