Question : Kajal can do a piece of work alone in 24 days, while Neha can do the same work alone in 40 days. Kajal started the work alone, and then after 12 clays, Neha joined her till the completion of the work. How long did the work take to be completed since Kajal started to work on it?
Option 1: $\frac{37}{4}$ days
Option 2: $\frac{39}{2}$ days
Option 3: $\frac{37}{2}$ days
Option 4: $\frac{39}{4}$ days
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Correct Answer: $\frac{39}{2}$ days
Solution : LCM of 24 and 40 = 120 Let the total work = 120 units Now, Kajal completes work in = 24 days Efficiency of Kajal = $\frac{120}{24}$ = 5 units/day Efficiency of Neha = $\frac{120}{40}$ = 3 units/day Kajal worked for 12 days before Neha Work done by Kajal = Efficiency × Number of days = 5 × 12 = 60 units Hence, 60 units of work are done by Kajal alone, Remaining work = (120 – 60) = 60 units Combined Efficiency of Kajal and Neha = (5 + 3) = 8 units/day Number of days = $\frac{60}{8}$ days = $\frac{15}{2}$ days Total number of days = $12 + \frac{15}{2}$ = $\frac{39}{2}$ days Hence, the correct answer is $\frac{39}{2}$ days.
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