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
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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