Certainly, let's solve each part of the question step-by-step.
### a) Mrs. Karki has a stationery shop and pays Rs 36,000 as house rent for every 3 months.
#### (i) How much rent does she pay in one year?
To determine the annual rent, we need to calculate how many 3-month periods there are in one year. There are 12 months in a year, so:
[tex]\[ \text{Number of 3-month periods in a year} = \frac{12 \text{ months}}{3 \text{ months per period}} = 4 \][/tex]
Since she pays Rs 36,000 for each 3-month period:
[tex]\[ \text{Annual rent} = 36,000 \times 4 = Rs 144,000 \][/tex]
So, Mrs. Karki pays Rs 144,000 in rent per year.
#### (ii) If the house owner increases the rent by Rs 2,000 per month, how much rent does she pay for every 3 months?
First, we calculate the total increase in rent for a 3-month period:
[tex]\[ \text{Monthly increase} = Rs 2,000 \][/tex]
[tex]\[ \text{3-month increase} = 2,000 \times 3 = Rs 6,000 \][/tex]
Adding this increase to the original 3-month rent:
[tex]\[ \text{New rent for every 3 months} = 36,000 + 6,000 = Rs 42,000 \][/tex]
So, after the increase, she now pays Rs 42,000 for every 3 months.
#### (iii) If the new house rent is [tex]\(\frac{1}{4}\)[/tex] part of her monthly profit, calculate her monthly profit.
First, we need to find the new monthly rent from the new 3-month rent:
[tex]\[ \text{New 3-month rent} = Rs 42,000 \][/tex]
[tex]\[ \text{New monthly rent} = \frac{42,000}{3} = Rs 14,000 \][/tex]
Given that this new monthly rent is [tex]\(\frac{1}{4}\)[/tex] of her monthly profit:
[tex]\[ \text{New Monthly Rent} = \frac{1}{4} \times \text{Monthly Profit} \][/tex]
[tex]\[ 14,000 = \frac{\text{Monthly Profit}}{4} \][/tex]
Solving for Monthly Profit:
[tex]\[ \text{Monthly Profit} = 14,000 \times 4 = Rs 56,000 \][/tex]
Thus, Mrs. Karki's monthly profit is Rs 56,000.
