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
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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