5) Anil can do a piece of work in 16 days which Shashi can
finish in 24 days. If they work on alternate days with Anil
starting, in how many days the work will be finished?
A) 15 days
B) 17 days
C) 18 days
D) 19 days
Answers
Ratio of efficiencies of Priya and Sai is
Sai : Priya = 160 : 100 = 8 : 5
Given Priya completes the work in 16 days
Let number of days Sai completes the work be 'd'
=> 5×16 = 8×d
d = 10 days.
Therefore, number of days Sai completes the work is 10 days.
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Given :-
- Anil can do a piece of work in = 16 days.
- Shashi can finish in = 24 days.
- Anil starts the work and the work on alternate days.
To Find :-
- In how many days the work will be finished ?
Solution :-
LCM of (16 and 24) = 48 units = Let total work .
so,
→ Efficiency of Anil = (Total work) / (Total days) = 48/16 = 3 unit/day .
→ Efficiency of Shashi = (Total work) / (Total days) = 48/24 = 2 unit/day .
then,
→ In first day, Anil completes work = 3 unit .
→ In second day, Shashi completes work = 2 unit .
therefore,
→ 5 units of work completes in = 2 days .
→ 45 units of work completes in = 2 * 9 = 18 days.
so ,
→ On 19th day , it turns of Anil now and he completes = 3 units .
∴
→ In 19 days work completes = 45 + 3 = 48 units = Total work.
Hence, The work will finished in 19 days.
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