Question : Rahul alone can complete a work in 10 days and Sonu alone can complete the same work in 15 days. If they work together for 4 days, then what part of total work is left?
Option 1: $\frac{2}{3}$
Option 2: $\frac{1}{5}$
Option 3: $\frac{1}{3}$
Option 4: $\frac{2}{5}$
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Correct Answer: $\frac{1}{3}$
Solution :
Time taken by Rahul to complete the work = 10 days
Time taken by Sonu to complete the work = 15 days
Let the total work = LCM of 18 and 15 = 90 units
Efficiency of Rahul = $\frac{90}{10}$ = 9 units/day
Efficiency of Sonu = $\frac{90}{15}$ = 6 units/day
Total Efficiency of Rahul and Sonu = 9 + 6 = 15 units/day
Work was completed by them in 4 days = 15 × 4 = 60 units
Remaining work = 90 – 60 = 30 units
Remaining part of the work left = $\frac{30}{90}$ = $\frac{1}{3}$
Hence, the correct answer is $\frac{1}{3}$.
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