Question : To do a certain work, the ratio of the efficiencies of A and B is 7 : 5. Working together, they can complete the same work in $17 \frac{1}{2}$ days. A alone will complete 60% of the same work in:
Option 1: 18 days
Option 2: 15 days
Option 3: 16 days
Option 4: 21 days
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Correct Answer: 18 days
Solution : Let the efficiency of A be $E_A$ and the efficiency of B as $E_B$. Given that the ratio of the efficiencies of A and B is 7 : 5, for some constant $x$. $E_A = 7x$ $E_B = 5x$ The total amount of work done by A and B together in one day. $E_A + E_B = 7x + 5x = 12x$ Given that A and B together can complete the work in $17\frac{1}{2}$ days. The total work $W$, $W = (E_A + E_B) \times \text{time} = 12x \times 17\frac{1}{2} = 210x$ The time it will take for A to complete 60% of the work alone. The amount of work A needs to do = $0.6W = 0.6 \times 210x = 126x$ The time it takes for A to complete this amount of work $=\frac{126x}{7x} = 18$ days Hence, the correct answer is 18 days.
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Question : Pawan can do a piece of work in 32 days. He worked for 8 days and left the work. Thereafter Sandeep finished the remaining work in 27 days. In how many days can Pawan and Sandeep together do the whole work?
Option 1: $16 \frac{16}{17}$ days
Option 2: $16 \frac{13}{17}$ days
Option 3: $16 \frac{15}{17}$ days
Option 4: $16 \frac{14}{17}$ days
Question : Raju and Rajat working together take 5 days to complete a piece of work. If Raju alone can do it in 7 days, how long would Rajat take to complete the same work?
Option 2: 16.5 days
Option 3: 17 days
Option 4: 17.5 days
Question : A, B, and C working alone, can complete a job in 16, 24, and 36 days, respectively. In how many days can they complete the job if they work together?
Option 1: $7 \frac{11}{19}$
Option 2: $5 \frac{17}{19}$
Option 3: $4 \frac{13}{19}$
Option 4: $6 \frac{7}{19}$
Question : A alone can do a work in 14 days. B alone can do the same work in 28 days. C alone can do the same work in 56 days. They started the work together and completed the work such that B was not working in the last 2 days and A did not work in the last 3 days. In how many days (total) was the work completed?
Option 1: $\frac{82}{7}$ days
Option 2: $\frac{79}{7}$ days
Option 3: $\frac{65}{7}$ days
Option 4: $\frac{72}{7}$ days
Question : A can do $\frac{1}{3}$ of a work in 30 days. B can do $\frac{2}{5}$ of the same work in 24 days. They worked together for 20 days. C completed the remaining work in 8 days. Working together A, B and C will complete the same work in:
Option 1: 15 days
Option 2: 10 days
Option 3: 18 days
Option 4: 12 days
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