Anthony spends `x%` of his salary towards expending on food , 2x% of the remaining on transport 3x% of the remaining towards various bills 4x% of the remaining towards loan repayments if the expenditures are denoted as F,T,B and L, respectively if x is 10 then what is the ascending order of these amounts?

Answer

To solve the problem step by step, we will calculate the expenditures on food (F), transport (T), bills (B), and loan repayments (L) based on the percentage of Anthony's salary he spends.

### Step 1: Determine the total salary
Let Anthony's total salary be represented as 100 units (for simplicity, since we are dealing with percentages).

### Step 2: Calculate expenditure on food (F)
Anthony spends \( x\% \) of his salary on food. Given \( x = 10 \):
\[ F = \frac{10}{100} \times 100 = 10 \text{ units} \]

### Step 3: Calculate remaining salary after food
After spending on food, the remaining salary is:
\[ \text{Remaining after food} = 100 - F = 100 - 10 = 90 \text{ units} \]

### Step 4: Calculate expenditure on transport (T)
Anthony spends \( 2x\% \) of the remaining salary on transport:
\[ T = \frac{2 \times 10}{100} \times 90 = \frac{20}{100} \times 90 = 18 \text{ units} \]

### Step 5: Calculate remaining salary after transport
The remaining salary after spending on transport is:
\[ \text{Remaining after transport} = 90 - T = 90 - 18 = 72 \text{ units} \]

### Step 6: Calculate expenditure on bills (B)
Anthony spends \( 3x\% \) of the remaining salary on bills:
\[ B = \frac{3 \times 10}{100} \times 72 = \frac{30}{100} \times 72 = 21.6 \text{ units} \]

### Step 7: Calculate remaining salary after bills
The remaining salary after spending on bills is:
\[ \text{Remaining after bills} = 72 - B = 72 - 21.6 = 50.4 \text{ units} \]

### Step 8: Calculate expenditure on loan repayments (L)
Anthony spends \( 4x\% \) of the remaining salary on loan repayments:
\[ L = \frac{4 \times 10}{100} \times 50.4 = \frac{40}{100} \times 50.4 = 20.16 \text{ units} \]

### Step 9: Summary of expenditures
Now we have the expenditures:
- F (Food) = 10 units
- T (Transport) = 18 units
- B (Bills) = 21.6 units
- L (Loan repayments) = 20.16 units

### Step 10: Ascending order of expenditures
To find the ascending order of these amounts:
- F = 10
- T = 18
- L = 20.16
- B = 21.6

Thus, the ascending order is:
\[ F < T < L < B \]