Antony spend one quarter of his net January salary on school fees he spent a quarter of the reminder on electricity bill and water he then spends one ninth of what was left on transport if he finally had sh.3400 calculate his net salary

fees: 1/4, leaving 3/4

utilities: 1/4 * 3/4 = 3/16, leaving 9/16
transport: 1/9 * 9/16 = 1/16, leaving 8/16 = 1/2
so, if his salary was x, then
1/2 x = 3400

Let's break down the problem step by step.

1. Antony spends one quarter of his net January salary on school fees.
Let's represent Antony's net salary as x.
Amount spent on school fees = (1/4) * x

2. He spends a quarter of the remainder on electricity bill and water.
After deducting the amount spent on school fees from his net salary, the remaining amount = x - (1/4) * x = (3/4) * x
Amount spent on electricity bill and water = (1/4) * (3/4) * x = (3/16) * x

3. He then spends one ninth of what was left on transport.
After deducting the amount spent on electricity bill and water, the remaining amount = (3/4) * x - (3/16) * x = (9/16) * x
Amount spent on transport = (1/9) * (9/16) * x = (1/16) * x

4. Finally, Antony has sh.3400 left.
The remaining amount after all expenses = (9/16) * x - (1/16) * x = (8/16) * x = (1/2) * x
(1/2) * x = sh.3400
x = sh.3400 * 2 = sh.6800

Therefore, Antony's net salary for January is sh.6800.

To calculate Antony's net salary, we need to work backward from the final amount of sh.3400 and reverse the calculations.

Let's break down the problem step by step:

1. Antony spent one-quarter of his net January salary on school fees.
If we denote Antony's net salary as "x", then the amount spent on school fees is (1/4) * x.

2. He spent a quarter of the remainder on the electricity bill and water.
After deducting the school fees, the remaining amount is (3/4) * x. Antony then spent (1/4) * ((3/4) * x) on electricity and water.

3. He spent one-ninth of what was left on transport.
After deducting the electricity and water bill, the remaining amount is (3/4) * x - (1/4) * ((3/4) * x). Antony spent (1/9) * ((3/4) * x - (1/4) * ((3/4) * x)) on transport.

4. Finally, we know that the remaining amount is sh.3400.
So, we have the following equation: (3/4) * x - (1/4) * ((3/4) * x) - (1/9) * ((3/4) * x - (1/4) * ((3/4) * x)) = 3400.

Now, let's solve this equation to find Antony's net salary "x".

(3/4) * x - (1/4) * ((3/4) * x) - (1/9) * ((3/4) * x - (1/4) * ((3/4) * x)) = 3400.

Simplifying the equation:
(3/4) * x - (1/4) * (3/4) * x - (1/9) * (3/4) * x + (1/9) * (1/4) * (3/4) * x = 3400.

Combining like terms:
(3/4) * x - (9/16) * x - (1/9) * (3/4) * x + (3/16) * x = 3400.

Finding the common denominator:
(12/16) * x - (9/16) * x - (3/16) * x + (3/16) * x = 3400.

Combining like terms:
(3/16) * x = 3400.

Multiplying both sides by (16/3):
x = (3400 * 16) / 3.

Calculating the value of x:
x = 18,133.33 shillings.

Therefore, Antony's net salary is sh.18,133.33.