A man spend 28% of his salary on food. From the remaining he spend 1/6 the on rent and send 3/8the to his mother. If he left with Rs. 5280, what amount he sends to his mother.

Options

A. Rs. 8230
B. Rs. 8640
C. Rs. 9580
D. Rs. 8420

Explanation

To solve the problem step by step, we will break down the expenses and calculate the amount sent to the mother.

### Step 1: Assume the Salary
Let's assume the man's salary is Rs. 100 (for easier calculations).

### Step 2: Calculate the Amount Spent on Food
The man spends 28% of his salary on food.
\[ \text{Amount spent on food} = 28\% \text{ of } 100 = 28 \]
Remaining salary after food:
\[ 100 - 28 = 72 \]

### Step 3: Calculate the Amount Spent on Rent
From the remaining amount, he spends \(\frac{1}{6}\) on rent.
\[ \text{Amount spent on rent} = \frac{1}{6} \text{ of } 72 = \frac{72}{6} = 12 \]
Remaining salary after rent:
\[ 72 - 12 = 60 \]

### Step 4: Calculate the Amount Sent to Mother
He sends \(\frac{3}{8}\) of the remaining amount to his mother.
\[ \text{Amount sent to mother} = \frac{3}{8} \text{ of } 60 = \frac{3 \times 60}{8} = \frac{180}{8} = 22.5 \]
Remaining salary after sending to mother:
\[ 60 - 22.5 = 37.5 \]

### Step 5: Set Up the Equation
According to the problem, he is left with Rs. 5280. Therefore, we can set up the equation:
\[ 37.5 \text{ units} = 5280 \]

### Step 6: Find the Value of 1 Unit
To find the value of 1 unit, we divide:
\[ \text{Value of 1 unit} = \frac{5280}{37.5} \]
Calculating this gives:
\[ \frac{5280}{37.5} = 140.8 \]

### Step 7: Calculate the Amount Sent to Mother
Now we need to find out how much he sends to his mother in actual currency:
\[ \text{Amount sent to mother} = 22.5 \text{ units} \times 140.8 \]
Calculating this gives:
\[ 22.5 \times 140.8 = 3168 \]

### Final Answer
The amount he sends to his mother is Rs. 3168.

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