Rahul can complete a work in 12 days and Ayush in 15 days. If they work together for 3 days, then the fraction of work that will be left is:
- A20
9
- B20
13
- C20
11
- D20
7
Solution & Step-by-step Explanation
Let the total work be the LCM of 12 and 15:
Total Work=LCM(12,15)=60 units
Now, find their daily rate of work (efficiencies):
Rahul’s efficiency=
12
60
=5 units/day
Ayush’s efficiency=
15
60
=4 units/day
Combined daily efficiency:
Combined efficiency=5+4=9 units/day
Work finished in 3 days:
Work Done=9×3=27 units
Remaining work:
Remaining Work=60−27=33 units
Fraction of work left:
Fraction left=
Total Work
Remaining Work
=
60
33
=
20
11
Total Work=LCM(12,15)=60 units
Now, find their daily rate of work (efficiencies):
Rahul’s efficiency=
12
60
=5 units/day
Ayush’s efficiency=
15
60
=4 units/day
Combined daily efficiency:
Combined efficiency=5+4=9 units/day
Work finished in 3 days:
Work Done=9×3=27 units
Remaining work:
Remaining Work=60−27=33 units
Fraction of work left:
Fraction left=
Total Work
Remaining Work
=
60
33
=
20
11