Menu Close

Five-engineers-A-B-C-D-and-E-can-complete-a-process-in-8-hours-assuming-that-every-engineer-works-with-the-same-efficiency-They-started-working-at-10-00am-If-after-4-00pm-one-engineer-is-removed

Tinku Tara 0 Comments
Pin




Question Number 15821 by chux last updated on 14/Jun/17
Five engineers A,B,C,D and E can complete a process in 8 hours, assuming that every engineer works with the same efficiency. They started working at 10:00am. If after 4:00pm..,one engineer is removed from the group every hour,what is the time when they will finish the work? (a)6:00pm (b)7:00pm (c)4:00pm (d)8:00pm
$$\mathrm{Five}\:\mathrm{engineers}\:\mathrm{A},\mathrm{B},\mathrm{C},\mathrm{D}\:\mathrm{and}\:\mathrm{E}\:\mathrm{can} \\ $$$$\mathrm{complete}\:\mathrm{a}\:\mathrm{process}\:\mathrm{in}\:\mathrm{8}\:\mathrm{hours}, \\ $$$$\mathrm{assuming}\:\mathrm{that}\:\mathrm{every}\:\mathrm{engineer}\: \\ $$$$\mathrm{works}\:\mathrm{with}\:\mathrm{the}\:\mathrm{same}\:\mathrm{efficiency}. \\ $$$$\mathrm{They}\:\mathrm{started}\:\mathrm{working}\:\mathrm{at}\:\mathrm{10}:\mathrm{00am}. \\ $$$$\mathrm{If}\:\mathrm{after}\:\mathrm{4}:\mathrm{00pm}..,\mathrm{one}\:\mathrm{engineer}\:\mathrm{is} \\ $$$$\mathrm{removed}\:\mathrm{from}\:\mathrm{the}\:\mathrm{group}\:\mathrm{every}\: \\ $$$$\mathrm{hour},\mathrm{what}\:\mathrm{is}\:\mathrm{the}\:\mathrm{time}\:\mathrm{when}\:\mathrm{they} \\ $$$$\mathrm{will}\:\mathrm{finish}\:\mathrm{the}\:\mathrm{work}? \\ $$$$\left(\mathrm{a}\right)\mathrm{6}:\mathrm{00pm} \\ $$$$\left(\mathrm{b}\right)\mathrm{7}:\mathrm{00pm} \\ $$$$\left(\mathrm{c}\right)\mathrm{4}:\mathrm{00pm} \\ $$$$\left(\mathrm{d}\right)\mathrm{8}:\mathrm{00pm} \\ $$
Commented by RasheedSoomro last updated on 14/Jun/17
Counting in hours. 40 hours are needed to complete the process. ( 8 hours of each of 5 engineers) ^• 10:00 to 4:00 (Duration 6 hours) 30 hours are spent (5 Engineers work ^• 4:00 to 5:00 4 hours are spent (∵ 4 engineers work) ^• 5:00 to 6:00 3 hours spent (3 engineers work) ^• 6:00 to 7:00 2 hours spent (2 engineers work ^• 7:00 to 8:00 1 hour spent (l engineer works) ^(• ) At 8:00 All engineers have gone to rest Total hours spent 40 hours Task of 40 hours completed on 8:00 5+5+5+5+5+5+4+3+2+1=40
$$\mathrm{Counting}\:\mathrm{in}\:\mathrm{hours}. \\ $$$$\:\mathrm{40}\:\mathrm{hours}\:\mathrm{are}\:\mathrm{needed}\:\mathrm{to}\:\mathrm{complete} \\ $$$$\mathrm{the}\:\mathrm{process}.\:\left(\:\mathrm{8}\:\mathrm{hours}\:\mathrm{of}\:\mathrm{each}\:\:\mathrm{of}\:\mathrm{5}\:\mathrm{engineers}\right) \\ $$$$ \\ $$$$\:^{\bullet} \mathrm{10}:\mathrm{00}\:\mathrm{to}\:\mathrm{4}:\mathrm{00}\:\left(\mathrm{Duration}\:\mathrm{6}\:\mathrm{hours}\right) \\ $$$$\mathrm{30}\:\mathrm{hours}\:\mathrm{are}\:\mathrm{spent}\:\left(\mathrm{5}\:\mathrm{Engineers}\:\mathrm{work}\right. \\ $$$$\:^{\bullet} \mathrm{4}:\mathrm{00}\:\mathrm{to}\:\mathrm{5}:\mathrm{00} \\ $$$$\mathrm{4}\:\mathrm{hours}\:\mathrm{are}\:\mathrm{spent}\:\left(\because\:\mathrm{4}\:\mathrm{engineers}\:\mathrm{work}\right) \\ $$$$\:^{\bullet} \mathrm{5}:\mathrm{00}\:\mathrm{to}\:\mathrm{6}:\mathrm{00} \\ $$$$\mathrm{3}\:\mathrm{hours}\:\mathrm{spent}\:\left(\mathrm{3}\:\mathrm{engineers}\:\mathrm{work}\right) \\ $$$$\:^{\bullet} \mathrm{6}:\mathrm{00}\:\mathrm{to}\:\mathrm{7}:\mathrm{00} \\ $$$$\mathrm{2}\:\mathrm{hours}\:\mathrm{spent}\:\left(\mathrm{2}\:\mathrm{engineers}\:\mathrm{work}\right. \\ $$$$\:^{\bullet} \mathrm{7}:\mathrm{00}\:\mathrm{to}\:\mathrm{8}:\mathrm{00} \\ $$$$\mathrm{1}\:\mathrm{hour}\:\mathrm{spent}\:\:\left(\mathrm{l}\:\mathrm{engineer}\:\mathrm{works}\right) \\ $$$$\:^{\bullet\:} \mathrm{At}\:\mathrm{8}:\mathrm{00} \\ $$$$\:\:\mathrm{All}\:\mathrm{engineers}\:\mathrm{have}\:\mathrm{gone}\:\mathrm{to}\:\mathrm{rest} \\ $$$$\:\:\:\mathrm{Total}\:\mathrm{hours}\:\mathrm{spent}\:\mathrm{40}\:\mathrm{hours} \\ $$$$\:\:\:\mathrm{Task}\:\mathrm{of}\:\mathrm{40}\:\mathrm{hours}\:\mathrm{completed}\:\mathrm{on}\:\mathrm{8}:\mathrm{00} \\ $$$$\mathrm{5}+\mathrm{5}+\mathrm{5}+\mathrm{5}+\mathrm{5}+\mathrm{5}+\mathrm{4}+\mathrm{3}+\mathrm{2}+\mathrm{1}=\mathrm{40} \\ $$
Commented by chux last updated on 14/Jun/17
i really appreciate this
$$\mathrm{i}\:\mathrm{really}\:\mathrm{appreciate}\:\mathrm{this} \\ $$
Answered by ajfour last updated on 14/Jun/17
Commented by RasheedSoomro last updated on 14/Jun/17
I always appreciate your skills to draw diagrams! (And of course geometrical skills & knowledge too!) Good luck my friend!
$$\mathrm{I}\:\mathrm{always}\:\mathrm{appreciate}\:\mathrm{your}\:\mathrm{skills}\:\mathrm{to} \\ $$$$\mathrm{draw}\:\mathrm{diagrams}! \\ $$$$\left(\mathrm{And}\:\mathrm{of}\:\mathrm{course}\:\mathrm{geometrical}\:\mathrm{skills}\:\&\right. \\ $$$$\left.\mathrm{knowledge}\:\mathrm{too}!\right) \\ $$$$\mathrm{Good}\:\mathrm{luck}\:\mathrm{my}\:\mathrm{friend}! \\ $$
Commented by ajfour last updated on 14/Jun/17
thanks a lot Sir, please view my solution to Q. 15828 ..i could prove that mainly because i extrapolated the medians of ΔABC.
$${thanks}\:{a}\:{lot}\:{Sir},\:{please}\:{view}\:{my} \\ $$$${solution}\:{to}\:{Q}.\:\mathrm{15828}\:..{i}\:{could} \\ $$$${prove}\:{that}\:{mainly}\:{because}\:{i} \\ $$$${extrapolated}\:{the}\:{medians}\: \\ $$$${of}\:\Delta{ABC}. \\ $$
Answered by mrW1 last updated on 14/Jun/17
each man can do each hour (1/(5×8))=(1/(40)) 10:00am−4:00pm: work done=5×6×(1/(40))=(3/4),rest=1−(3/4)=(1/4) 4:00pm−5:00pm: work done=4×1×(1/(40))=(1/(10)),rest=(1/4)−(1/(10))=(3/(20)) 5:00pm−6:00pm: work done=3×1×(1/(40))=(3/(40)),rest=(3/(20))−(3/(40))=(3/(40)) 6:00pm−7:00pm: work done=2×1×(1/(40))=(1/(20)),rest=(3/(40))−(1/(20))=(1/(40)) 7:00pm−8:00pm: work done=1×1×(1/(40))=(1/(40)),rest=(1/(40))−(1/(40))=0 ⇒at 8:00pm the work is completely done. ⇒answer (d)
$$\mathrm{each}\:\mathrm{man}\:\mathrm{can}\:\mathrm{do}\:\mathrm{each}\:\mathrm{hour}\:\frac{\mathrm{1}}{\mathrm{5}×\mathrm{8}}=\frac{\mathrm{1}}{\mathrm{40}} \\ $$$$\mathrm{10}:\mathrm{00am}−\mathrm{4}:\mathrm{00pm}: \\ $$$$\mathrm{work}\:\mathrm{done}=\mathrm{5}×\mathrm{6}×\frac{\mathrm{1}}{\mathrm{40}}=\frac{\mathrm{3}}{\mathrm{4}},\mathrm{rest}=\mathrm{1}−\frac{\mathrm{3}}{\mathrm{4}}=\frac{\mathrm{1}}{\mathrm{4}} \\ $$$$\mathrm{4}:\mathrm{00pm}−\mathrm{5}:\mathrm{00pm}: \\ $$$$\mathrm{work}\:\mathrm{done}=\mathrm{4}×\mathrm{1}×\frac{\mathrm{1}}{\mathrm{40}}=\frac{\mathrm{1}}{\mathrm{10}},\mathrm{rest}=\frac{\mathrm{1}}{\mathrm{4}}−\frac{\mathrm{1}}{\mathrm{10}}=\frac{\mathrm{3}}{\mathrm{20}} \\ $$$$\mathrm{5}:\mathrm{00pm}−\mathrm{6}:\mathrm{00pm}: \\ $$$$\mathrm{work}\:\mathrm{done}=\mathrm{3}×\mathrm{1}×\frac{\mathrm{1}}{\mathrm{40}}=\frac{\mathrm{3}}{\mathrm{40}},\mathrm{rest}=\frac{\mathrm{3}}{\mathrm{20}}−\frac{\mathrm{3}}{\mathrm{40}}=\frac{\mathrm{3}}{\mathrm{40}} \\ $$$$\mathrm{6}:\mathrm{00pm}−\mathrm{7}:\mathrm{00pm}: \\ $$$$\mathrm{work}\:\mathrm{done}=\mathrm{2}×\mathrm{1}×\frac{\mathrm{1}}{\mathrm{40}}=\frac{\mathrm{1}}{\mathrm{20}},\mathrm{rest}=\frac{\mathrm{3}}{\mathrm{40}}−\frac{\mathrm{1}}{\mathrm{20}}=\frac{\mathrm{1}}{\mathrm{40}} \\ $$$$\mathrm{7}:\mathrm{00pm}−\mathrm{8}:\mathrm{00pm}: \\ $$$$\mathrm{work}\:\mathrm{done}=\mathrm{1}×\mathrm{1}×\frac{\mathrm{1}}{\mathrm{40}}=\frac{\mathrm{1}}{\mathrm{40}},\mathrm{rest}=\frac{\mathrm{1}}{\mathrm{40}}−\frac{\mathrm{1}}{\mathrm{40}}=\mathrm{0} \\ $$$$\Rightarrow\mathrm{at}\:\mathrm{8}:\mathrm{00pm}\:\mathrm{the}\:\mathrm{work}\:\mathrm{is}\:\mathrm{completely}\:\mathrm{done}. \\ $$$$\Rightarrow\mathrm{answer}\:\left(\mathrm{d}\right) \\ $$
Commented by chux last updated on 14/Jun/17
I must confess I′ve learnt so much from you.Thank you so much.
$$\:\mathrm{I}\:\mathrm{must} \\ $$$$\mathrm{confess}\:\mathrm{I}'\mathrm{ve}\:\mathrm{learnt}\:\mathrm{so}\:\mathrm{much}\:\mathrm{from} \\ $$$$\mathrm{you}.\mathrm{Thank}\:\mathrm{you}\:\mathrm{so}\:\mathrm{much}. \\ $$$$ \\ $$

Pin

Leave a Reply

Your email address will not be published. Required fields are marked *