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