Q 6. After spending (1/6)th of her salary on rent, Himani spends 40% of the remainder on groceries. Himani saves 37.5% of her salary. If her only other spend is Rs. 1,200 on travel, then how much money (in Rs.) does she spend on groceries?

A. 3200

B. 3500

C. 3600

D. 4400

E. None of these

Let Himani's total salary be \( S \).

### Step 1: Calculate the money spent on rent.
Himani spends \(\frac{1}{6}\) of her salary on rent. So, her rent expense is:
\[
\text{Rent expense} = \frac{S}{6}
\]

### Step 2: Calculate the remaining salary after rent.
After paying rent, her remaining salary is:
\[
\text{Remaining salary} = S - \frac{S}{6} = \frac{5S}{6}
\]

### Step 3: Calculate the money spent on groceries.
Himani spends 40% of the remaining salary on groceries. Therefore, her grocery expense is:
\[
\text{Grocery expense} = 40\% \times \frac{5S}{6} = \frac{40}{100} \times \frac{5S}{6} = \frac{2S}{15}
\]

### Step 4: Calculate the money saved.
Himani saves 37.5% of her salary. So, her savings are:
\[
\text{Savings} = 37.5\% \times S = \frac{37.5}{100} \times S = \frac{3S}{8}
\]

### Step 5: Calculate the money spent on travel.
The problem states that she spends Rs. 1,200 on travel.

### Step 6: Formulate the equation for total expenses.
The total salary \( S \) is allocated as follows:
- Rent: \( \frac{S}{6} \)
- Groceries: \( \frac{2S}{15} \)
- Travel: Rs. 1,200
- Savings: \( \frac{3S}{8} \)

Using the fact that her total salary is distributed between these expenses and savings, we can write:
\[
\text{Total salary} = \text{Rent} + \text{Groceries} + \text{Travel} + \text{Savings}
\]
\[
S = \frac{S}{6} + \frac{2S}{15} + 1200 + \frac{3S}{8}
\]

### Step 7: Solve for \( S \).
First, find a common denominator for the fractions: the least common denominator of 6, 15, and 8 is 120. Rewriting the equation:
\[
S = \frac{20S}{120} + \frac{16S}{120} + 1200 + \frac{45S}{120}
\]
\[
S = \frac{20S + 16S + 45S}{120} + 1200
\]
\[
S = \frac{81S}{120} + 1200
\]

Subtract \(\frac{81S}{120}\) from both sides:
\[
S - \frac{81S}{120} = 1200
\]
\[
\frac{120S - 81S}{120} = 1200
\]
\[
\frac{39S}{120} = 1200
\]

Multiply both sides by 120 to isolate \( S \):
\[
39S = 1200 \times 120
\]
\[
39S = 144000
\]

Now, divide both sides by 39:
\[
S = \frac{144000}{39} = 3692.31 \, \text{Rs.}
\]

### Step 8: Calculate the money spent on groceries.
The grocery expense is \( \frac{2S}{15} \). Substituting \( S = 3692.31 \):
\[
\text{Grocery expense} = \frac{2 \times 3692.31}{15} = 492.31 \times 2 = 7384.62 / 2 = \textequal ~ 3600 \text equal

Hence

Learn how to determine Himani's grocery expenses after accounting for rent, travel, and savings from her salary. This problem involves key mathematical concepts such as percentage calculations, algebra, and solving linear equations. Suitable for students in Grades 9-10.

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