Question
P and Q can do a work in 30 days. Q and R can do the same work in 24 days and R and P in 20 days. They started the work together, but Q and R left after 10 days. How many days more will P take to finish the work?
Answer: Option C
LET WORK DONE BY P IN 1 DAY = P,
WORK DONE BY Q IN 1 DAY = Q,
WORK DONE BY R IN 1 DAY = R
P + Q = 1/30
Q + R = 1/24
R + P = 1/20
ADDING ALL THE ABOVE, 2P + 2Q + 2R = 1/30 + 1/24+ 1/20 = 15/120 = 1/8
=> P + Q + R = 1/16
=> WORK DONE BY P,Q AND R IN 1 DAY = 1/16
WORK DONE BY P, Q AND R IN 10 DAYS = 10 × (1/16) = 10/16 = 5/8
REMAINING WORK = 1 = 5/8 = 3/8
WORK DONE BY P IN 1 DAY = WORK DONE BY P,Q AND R IN 1 DAY – WORK DONE BY Q AND R IN 1 DAY
= 1/16 – 1/24 = 1/48
NUMBER OF DAYS P NEEDS TO WORK TO COMPLETE THE REMAINING WORK = (3/8) / (1/48) = 18
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LET WORK DONE BY P IN 1 DAY = P,
WORK DONE BY Q IN 1 DAY = Q,
WORK DONE BY R IN 1 DAY = R
P + Q = 1/30
Q + R = 1/24
R + P = 1/20
ADDING ALL THE ABOVE, 2P + 2Q + 2R = 1/30 + 1/24+ 1/20 = 15/120 = 1/8
=> P + Q + R = 1/16
=> WORK DONE BY P,Q AND R IN 1 DAY = 1/16
WORK DONE BY P, Q AND R IN 10 DAYS = 10 × (1/16) = 10/16 = 5/8
REMAINING WORK = 1 = 5/8 = 3/8
WORK DONE BY P IN 1 DAY = WORK DONE BY P,Q AND R IN 1 DAY – WORK DONE BY Q AND R IN 1 DAY
= 1/16 – 1/24 = 1/48
NUMBER OF DAYS P NEEDS TO WORK TO COMPLETE THE REMAINING WORK = (3/8) / (1/48) = 18
Was this answer helpful ?
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