A person gives `30% ` of his income to his elder daughter and `40% `of remaining to his younger daughter. And he distribute rest of the money equally among his 3 sons. If each son got Rs. 672, then how much money did the elder and younger daughter got?

Answer

To solve the problem, we will break it down step by step.

**Step 1: Define the total income.**
Let the total income of the person be \( I \).

**Step 2: Calculate the amount given to the elder daughter.**
The elder daughter receives 30% of the total income:
\[ \text{Amount to elder daughter} = 0.30 \times I \]

**Step 3: Calculate the remaining income after giving to the elder daughter.**
After giving 30% to the elder daughter, the remaining income is:
\[ \text{Remaining income} = I - 0.30 \times I = 0.70 \times I \]

**Step 4: Calculate the amount given to the younger daughter.**
The younger daughter receives 40% of the remaining income:
\[ \text{Amount to younger daughter} = 0.40 \times (0.70 \times I) = 0.28 \times I \]

**Step 5: Calculate the remaining income after giving to the younger daughter.**
After giving to the younger daughter, the remaining income is:
\[ \text{Remaining income} = 0.70 \times I - 0.28 \times I = 0.42 \times I \]

**Step 6: Distribute the remaining income among the 3 sons.**
The remaining income is distributed equally among 3 sons, so each son receives:
\[ \text{Amount each son gets} = \frac{0.42 \times I}{3} = 0.14 \times I \]

**Step 7: Set up the equation based on the amount each son received.**
We know that each son received Rs. 672:
\[ 0.14 \times I = 672 \]

**Step 8: Solve for the total income \( I \).**
To find \( I \), we rearrange the equation:
\[ I = \frac{672}{0.14} = 4800 \]

**Step 9: Calculate the amounts received by the elder and younger daughters.**
Now that we have \( I \), we can calculate the amounts received by each daughter:
- Amount to elder daughter:
\[ \text{Amount to elder daughter} = 0.30 \times 4800 = 1440 \]
- Amount to younger daughter:
\[ \text{Amount to younger daughter} = 0.28 \times 4800 = 1344 \]

**Final Answer:**
- The elder daughter received Rs. 1440.
- The younger daughter received Rs. 1344.

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