Out of her monthly salary Ridhi spends `34%`.on various expenses. From the remaining, she gives `1/6`th to her brother,`2/3` to her sister and the remaining she keeps as savings. If the difference between the amounts she gave to her sister and brother was ₹10,560, what was Ridhi’s savings?

Options

A. ₹ 3,420
B. ₹ 4,230
C. ₹ 3,230
D. Other than those given as options

Answer

To solve the problem step-by-step, we will follow the logical deductions based on the information provided.

### Step 1: Define Ridhi's Monthly Salary
Let Ridhi's monthly salary be represented as \( S \). For ease of calculation, we can express it as \( S = 100x \), where \( x \) is a variable that will help us simplify the percentages.

### Step 2: Calculate Ridhi's Expenses
Ridhi spends \( 34\% \) of her salary on various expenses. Therefore, the amount spent on expenses is:
\[ \text{Expenses} = 34\% \text{ of } S = \frac{34}{100} \times S = 34x \]

### Step 3: Calculate Remaining Amount After Expenses
The remaining amount after expenses can be calculated as:
\[ \text{Remaining} = S - \text{Expenses} = 100x - 34x = 66x \]

### Step 4: Distribute the Remaining Amount
From the remaining amount, Ridhi gives:
- \( \frac{1}{6} \) to her brother
- \( \frac{2}{3} \) to her sister

Calculating the amounts given:
- Amount to brother:
\[ \text{Brother's Share} = \frac{1}{6} \times 66x = 11x \]
- Amount to sister:
\[ \text{Sister's Share} = \frac{2}{3} \times 66x = 44x \]

### Step 5: Calculate the Difference Between Sister's and Brother's Amounts
According to the problem, the difference between the amounts given to her sister and brother is ₹10,560:
\[ \text{Difference} = \text{Sister's Share} - \text{Brother's Share} = 44x - 11x = 33x \]
Setting this equal to ₹10,560 gives us:
\[ 33x = 10,560 \]

### Step 6: Solve for \( x \)
To find \( x \), we divide both sides by 33:
\[ x = \frac{10,560}{33} = 320 \]

### Step 7: Calculate Ridhi's Savings
Now, we can calculate Ridhi's savings. The total amount given to her brother and sister is:
\[ \text{Total Given} = 11x + 44x = 55x \]
The savings can be calculated as:
\[ \text{Savings} = \text{Remaining} - \text{Total Given} = 66x - 55x = 11x \]
Substituting the value of \( x \):
\[ \text{Savings} = 11 \times 320 = 3520 \]

### Final Answer
Ridhi's savings amount to ₹3,520.

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