Ajeeta and Sanjeeta undertake a project for ₹ 48000. Further, it is known that Ajeeta can finish the project in 24 days and Sanjeeta can finish the project in 40 days while working alone. If the project gets completed in just 10 days when Ranjeeta also helped them in completing the project, then determine the amount that Ranjeeta would have received, if they distributed the amount in proportion to their respective working capability?

Ajeeta can finish the project in 24 days, so Ajeeta's work rate = $\frac{1}{24}$ of the project per day.

Sanjeeta can finish the project in 40 days, so Sanjeeta's work rate = $\frac{1}{40}$ of the project per day.

All three together complete the project in 10 days, so their combined work rate = $\frac{1}{10}$ of the project per day.

---

Ranjeeta's work rate = Combined rate - Ajeeta's rate - Sanjeeta's rate

Ranjeeta's rate = $\frac{1}{10} - \frac{1}{24} - \frac{1}{40}$

Converting to common denominator (LCM of 10, 24, 40 = 120):

$\frac{1}{10} = \frac{12}{120}$

$\frac{1}{24} = \frac{5}{120}$

$\frac{1}{40} = \frac{3}{120}$

Ranjeeta's rate = $\frac{12}{120} - \frac{5}{120} - \frac{3}{120}$

Ranjeeta's rate = $\frac{4}{120} = \frac{1}{30}$ per day

---

Work done by each person in 10 days:

Ajeeta's work = $\frac{1}{24} \times 10$

$= \frac{10}{24}$

$= \frac{5}{12}$

Sanjeeta's work = $\frac{1}{40} \times 10$

$= \frac{10}{40}$

$= \frac{3}{12}$

Ranjeeta's work = $\frac{1}{30} \times 10$

$= \frac{10}{30}$

$= \frac{4}{12}$

---

Work ratio = Ajeeta : Sanjeeta : Ranjeeta

$= \frac{5}{12} : \frac{3}{12} : \frac{4}{12}$

$= 5 : 3 : 4$

Total parts = $5 + 3 + 4 = 12$

---

Ranjeeta's share = $\frac{4}{12} \times 48000$

$= 4 \times 4000$

$= 16000$

Therefore, Ranjeeta receives ₹16,000.