Rapunzel and Harley Quinn, working for 8 hours a day, can independently do a piece of work in 15 days and 12
days respectively. They work in shifts - 8:00 a.m. to 1:00p.m. (morning shift) and 2:00 p.m. to 5:00p.m. (afternoon
shift). On the first day, Rapunzel works in the morning shift while Harley Quinn works in the afternoon shift. On
the second day, Harley Quinn works in the morning shift, and Rapunzel works in the afternoon shift. This pattern
of alternating shifts continues until the work is completed. When does the work get completed?
15th day
14th day
12th day
13th day
Answers
Answer :-
LCM of 15 and 12 = 60 units = Let total work .
so,
→ Efficiency of Rapunzel = 60/15 = 4 units / day .
now, given that, 1 day = 8 hours .
so,
→ In 8 hours Rapunzel do = 4 units
→ In 1 hour Rapunzel do = (4/8) = (1/2) units / hour .
similarly,
→ Efficiency of Harley Quinn = 60/12 = 5 units / day .
so,
→ In 1 hour harley do = (5/8) units / hour .
Now,
→ First day works completes = 5 * Rapunzel + 3 Harley = 5(1/2) + 3(5/8) = (5/2) + (15/8) = (35/8) units .
and,
→ Second day work completes = 5 * harley + 3 * rapunzel = 5(5/8) + 3(1/2) = (25/8) + (3/2) = (37/8) units .
then,
→ In 2 days work is completed = (35/8) + (37/8) = (72/8) = 9 units .
therefore,
→ 9 units completes in = 2 days
→ 9 * 6 units completes in = 2 * 6
→ 54 units will complete in = 12 days .
now,
→ Left work to be complete = 60 - 54 = 6 units .
on 13th day , Rapunzel works in the morning shift while Harley Quinn works in the afternoon shift.
so,
→ work completes on 13th day = 5(1/2) + 3(5/8) = (35/8) units .
then,
→ Left work to be complete = 6 - (35/8) = (13/8) units .
On 14th day Harley Quinn starts work in morning shift and left work is (13/8) units .
so,
→ Time taken by harley = (13/8) / (5/8) = (13/5) = 2.6 hours .
Hence,
→ whole work will completes in = 14 days + 2.6 hours = 14 days 2 hours and 36 minutes .
∴ The work get completed on 15th day .
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