Question : Pia and Ria can complete a project together in 26 days. Pia alone can complete the project in 78 days. They start working together but Pia leaves after 12 days. In how many days can Ria complete the remaining work of the project?
Option 1: 21 days
Option 2: 24 days
Option 3: 25 days
Option 4: 13 days
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Correct Answer: 21 days
Solution : Work done by Pia + Ria = 26 days Work done by Pia = 78 days LCM of 26 and 78 is 78 Total work = 78 units Efficiency of Pia and Ria = $\frac{78}{26} = 3$ Efficiency of Pia = $\frac{78}{78} = 1$ Efficiency of Ria = 3 – 1 = 2 Work done by Pia and Ria in 12 days = 3 × 12 = 36 unit Remaining work = 78 – 36 = 42 unit Number of days Ria takes to complete the remaining work = $\frac{\text{Total work}}{\text{Efficiency}}=\frac{42}{2}= 21$ Hence, the correct answer is 21 days.
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Question : S alone can do a piece of work in 14 days. T alone can do the same work in 21 days. U alone can do the same work in 28 days. Working together, in how many days will they complete the work?
Option 1: $\frac{84}{13}$ days
Option 2: $\frac{77}{13}$ days
Option 3: $\frac{71}{13}$ days
Option 4: $\frac{87}{13}$ days
Question : P alone can complete a work in 15 days and Q alone can complete the same work in 12 days. They start the work together but after 3 days P leaves the work. How much time will Q take to finish the remaining work?
Option 1: 7.2 days
Option 2: 7.8 days
Option 3: 8.5 days
Option 4: 6.6 days
Question : A alone can complete a work in 16 days and B alone can complete the same work in 96 days. In how many days both A and B together can complete the same work?
Option 1: $\frac{88}{13}$ days
Option 2: $\frac{96}{7}$ days
Option 3: $\frac{96}{13}$ days
Option 4: $\frac{88}{14}$ days
Question : Rimmi and Simmi can together finish a work in 40 days. They worked together for 30 days and then Simmi left. After another 30 days, Rimmi finished the remaining work alone. In how many days Rimmi alone can finish the work?
Option 1: 120 days
Option 2: 30 days
Option 3: 80 days
Option 4: 40 days
Question : P alone can do a piece of work in 24 days. Q alone can do it in 30 days and R alone can do it in 20 days. In how many days they can complete it together?
Option 1: 15 days
Option 2: 18 days
Option 3: 8 days
Option 4: 10 days
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