Suppose five friends Ritu, Mohani, Aman, Sam and Kiran are appointed to complete a certain piece of work. Ram and Mohani together can complete a work in 24 days. Mohani and Aman together can complete 50% of the work in 15 days. Aman and Sam together can complete the work in 24 days. Ritu and Kiran together can complete 16.66% of the work in 6 days. Sam and Kiran together can complete the work in 20 days. Suppose Bittu is 50% more efficient than Aman then, what will be the time taken by Bittu alone to complete 40% of the work.

### Concept & Time and Work To find the time taken by a specific person, we must determine their individual 1-day work (efficiency). We can find this by creating a system of linear equations based on the combined efficiencies given in the problem. $$ \text{Work done in 1 day} = \frac{1}{\text{Total days to complete work}} $$ ### Step-by-Step Solution Given combined work rates (Assuming Ram refers to Ritu based on logical deduction of standard puzzle structures): * Ram (Ritu) + Mohani = $1/24$ of work per day. * Mohani + Aman = $50\%$ in 15 days = $100\%$ in 30 days $\rightarrow 1/30$ per day. * Aman + Sam = $1/24$ of work per day. * Ritu + Kiran = $16.66\%$ (which is $1/6$) in 6 days = $100\%$ in 36 days $\rightarrow 1/36$ per day. * Sam + Kiran = $1/20$ of work per day. We need Aman's efficiency ($A$). Let's assign variables: $R+M = 1/24$, $M+A = 1/30$, $A+S = 1/24$, $S+K = 1/20$, $R+K = 1/36$. Calculate $(M+A) - (A+S) + (S+K) - (R+K)$: $M - R = \frac{1}{30} - \frac{1}{24} + \frac{1}{20} - \frac{1}{36}$ $M - R = \frac{12 - 15 + 18 - 10}{360} = \frac{5}{360} = \frac{1}{72}$ We know $R + M = 1/24 = 3/72$. Adding these two equations: $2M = \frac{1}{72} + \frac{3}{72} = \frac{4}{72} = \frac{1}{18}$ $M = \frac{1}{36}$ Now substitute $M$ into the $M+A$ equation to find $A$: $\frac{1}{36} + A = \frac{1}{30}$ $A = \frac{1}{30} - \frac{1}{36} = \frac{6 - 5}{180} = \frac{1}{180}$ Aman takes 180 days to complete the work. Bittu is $50\%$ more efficient than Aman. Bittu's 1-day work = $1.5 \times \frac{1}{180} = \frac{3}{2} \times \frac{1}{180} = \frac{1}{120}$ Bittu takes 120 days to complete the whole work. Time to complete $40\%$ of the work = $0.40 \times 120 = 48$ days. ### Exam Strategy & Shortcut Instead of solving for every single variable, selectively add and subtract the combined equations to isolate exactly the variables you need (like $M-R$ to combine with $M+R$). This cuts calculation time in half. ### Common Pitfall A frequent mistake is applying the $50\%$ efficiency directly to the days rather than the work rate. Remember that efficiency is inversely proportional to time: $50\%$ more efficient means multiplying the work rate by $1.5$, not multiplying the total days by $1.5$. ### Final Answer Therefore, the correct answer is **48 days**.