Question : Numan does half the work of Gagan in $\frac{4}{5}$ time. If they together take 16 days to complete a work, how much time will Gagan take to complete the work?
Option 1: 23 days
Option 2: 24 days
Option 3: 25 days
Option 4: 26 days
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Correct Answer: 26 days
Solution :
According to the question,
Numan $× \frac{4}{5}$ = Gagan $× \frac{1}{2}$
⇒ Numan = Gagan $× \frac{5}{8}$
⇒ $\frac{\text{Numan}}{\text{Gagan}} = \frac{5}{8}$
Let Numan’s efficiency = 5 units/day
And, Gagan’s efficiency = 8 units/day
So, the total work $= 16 × (5 + 8)=16 × 13$ units
Therefore, time taken by Gagan $= \frac{16 × 13}{8}=26$ Days
Hence, the correct answer is 26 days.
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