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?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → ₹16000
Given:
- Total amount = ₹48000
- Ajeeta alone: 24 days → work/day = 1/24
- Sanjeeta alone: 40 days → work/day = 1/40
- Project completed in 10 days with Ranjeeta
Total work = 1 unit
Let Ranjeeta's 1-day work = r
Total work in 10 days:
$10 \left( \frac{1}{24} + \frac{1}{40} + r \right) = 1$
LCM(24, 40) = 120
$\frac{1}{24} + \frac{1}{40} = \frac{5+3}{120} = \frac{2}{30} = \frac{4}{60}$
So, $10\left( \frac{1}{24} + \frac{1}{40} + r \right) = 1$
$\Rightarrow \left( \frac{1}{24} + \frac{1}{40} + r \right) = \frac{1}{10}$
$\Rightarrow r = \frac{1}{10} - \left( \frac{1}{24} + \frac{1}{40} \right) = \frac{1}{10} - \frac{1}{15} = \frac{3-2}{30} = \frac{1}{30}$
Work done in 10 days:
- Ajeeta: $10 \times \frac{1}{24} = \frac{5}{12}$
- Sanjeeta: $10 \times \frac{1}{40} = \frac{1}{4}$
- Ranjeeta: $10 \times \frac{1}{30} = \frac{1}{3}$
Total shares ratio: $\frac{5}{12} : \frac{1}{4} : \frac{1}{3}$
LCM of denominators = 12
Convert to same denominator: $\frac{5}{12} : \frac{3}{12} : \frac{4}{12} = 5 : 3 : 4$
Total parts = 5 + 3 + 4 = 12
Ranjeeta's share = $\frac{4}{12} \times 48000 = ₹16000$