Step 1: Capital balance on date of death = ₹3,00,000
Step 2: Interest on capital for 6 months (from 1st April to 1st October)
Interest = ₹3,00,000 × 10% × \( \frac{6}{12} \) = ₹15,000
Step 3: Share in General Reserve
Total reserve = ₹60,000
Chandni’s share = \( \frac{5}{10} \times 60,000 = ₹30,000 \)
Step 4: Share in Goodwill
Goodwill of firm = ₹1,20,000
Chandni’s share = \( \frac{5}{10} \times 1,20,000 = ₹60,000 \)
Step 5: Share in Profit till date of death (6 months)
Previous year’s profit = ₹4,50,000
Profit for 6 months = ₹4,50,000 × \( \frac{6}{12} \) = ₹2,25,000
Chandni’s share = \( \frac{5}{10} \times 2,25,000 = ₹1,12,500 \)
Step 6: Total Due to Chandni’s Executors:
| Particulars | Amount (₹) |
|---|---|
| Capital Balance | 3,00,000 |
| Add: Interest on Capital | 15,000 |
| Add: Share of General Reserve | 30,000 |
| Add: Share of Goodwill | 60,000 |
| Add: Share of Profit till death | 1,12,500 |
| Total Amount Payable | 5,17,500 |

A ladder of fixed length \( h \) is to be placed along the wall such that it is free to move along the height of the wall.
Based upon the above information, answer the following questions:
(iii) (b) If the foot of the ladder, whose length is 5 m, is being pulled towards the wall such that the rate of decrease of distance \( y \) is \( 2 \, \text{m/s} \), then at what rate is the height on the wall \( x \) increasing when the foot of the ladder is 3 m away from the wall?