A father gives `1%` of his monthly income to his 2 sons. He gives `80% ` of that amount to his elder son. From which he spends `80% ` of the amount that he acquires and his monthly saving remains Rs 20. Find the income of father

Answer

To solve the problem step by step, let's denote the father's monthly income as \( I \).

### Step 1: Calculate the amount given to the sons
The father gives \( 1\% \) of his monthly income to his sons:
\[ \text{Amount given to sons} = \frac{1}{100} \times I = 0.01I \]

### Step 2: Calculate the amount given to the elder son
Out of the total amount given to the sons, the father gives \( 80\% \) to the elder son:
\[ \text{Amount given to elder son} = 0.80 \times 0.01I = 0.008I \]

### Step 3: Calculate the amount spent by the elder son
The elder son spends \( 80\% \) of the amount he receives:
\[ \text{Amount spent by elder son} = 0.80 \times 0.008I = 0.0064I \]

### Step 4: Calculate the savings of the elder son
The elder son saves \( 20 \) rupees from the amount he receives:
\[ \text{Savings of elder son} = \text{Amount given to elder son} - \text{Amount spent by elder son} \]
\[ 20 = 0.008I - 0.0064I \]
\[ 20 = 0.0016I \]

### Step 5: Solve for the father's monthly income
To find \( I \), we rearrange the equation:
\[ I = \frac{20}{0.0016} \]
Calculating this gives:
\[ I = 12500 \]

Thus, the father's monthly income is \( \text{Rs } 12500 \).

### Final Answer:
The income of the father is Rs 12500.

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