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

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Question Number 15821 by chux last updated on 14/Jun/17

$$\mathrm{Five}\mathrm{engineers}\mathrm{A},\mathrm{B},\mathrm{C},\mathrm{D}\mathrm{and}\mathrm{E}\mathrm{can}$$$$\mathrm{complete}\mathrm{a}\mathrm{process}\mathrm{in}8\mathrm{hours},$$$$\mathrm{assuming}\mathrm{that}\mathrm{every}\mathrm{engineer}$$$$\mathrm{works}\mathrm{with}\mathrm{the}\mathrm{same}\mathrm{efficiency}.$$$$\mathrm{They}\mathrm{started}\mathrm{working}\mathrm{at}10:00\mathrm{am}.$$$$\mathrm{If}\mathrm{after}4:00\mathrm{pm}..,\mathrm{one}\mathrm{engineer}\mathrm{is}$$$$\mathrm{removed}\mathrm{from}\mathrm{the}\mathrm{group}\mathrm{every}$$$$\mathrm{hour},\mathrm{what}\mathrm{is}\mathrm{the}\mathrm{time}\mathrm{when}\mathrm{they}$$$$\mathrm{will}\mathrm{finish}\mathrm{the}\mathrm{work}?$$$$\left(\mathrm{a}\right)6:00\mathrm{pm}$$$$\left(\mathrm{b}\right)7:00\mathrm{pm}$$$$\left(\mathrm{c}\right)4:00\mathrm{pm}$$$$\left(\mathrm{d}\right)8:00\mathrm{pm}$$

Commented by RasheedSoomro last updated on 14/Jun/17

$$\mathrm{Counting}\mathrm{in}\mathrm{hours}.$$$$40\mathrm{hours}\mathrm{are}\mathrm{needed}\mathrm{to}\mathrm{complete}$$$$\mathrm{the}\mathrm{process}.\left(8\mathrm{hours}\mathrm{of}\mathrm{each}\mathrm{of}5\mathrm{engineers}\right)$$$$$$$${}^{\bullet }10:00\mathrm{to}4:00\left(\mathrm{Duration}6\mathrm{hours}\right)$$$$30\mathrm{hours}\mathrm{are}\mathrm{spent}(5\mathrm{Engineers}\mathrm{work}$$$${}^{\bullet }4:00\mathrm{to}5:00$$$$4\mathrm{hours}\mathrm{are}\mathrm{spent}(\because 4\mathrm{engineers}\mathrm{work})$$$${}^{\bullet }5:00\mathrm{to}6:00$$$$3\mathrm{hours}\mathrm{spent}\left(3\mathrm{engineers}\mathrm{work}\right)$$$${}^{\bullet }6:00\mathrm{to}7:00$$$$2\mathrm{hours}\mathrm{spent}(2\mathrm{engineers}\mathrm{work}$$$${}^{\bullet }7:00\mathrm{to}8:00$$$$1\mathrm{hour}\mathrm{spent}\left(\mathrm{l}\mathrm{engineer}\mathrm{works}\right)$$$${}^{\bullet }\mathrm{At}8:00$$$$\mathrm{All}\mathrm{engineers}\mathrm{have}\mathrm{gone}\mathrm{to}\mathrm{rest}$$$$\mathrm{Total}\mathrm{hours}\mathrm{spent}40\mathrm{hours}$$$$\mathrm{Task}\mathrm{of}40\mathrm{hours}\mathrm{completed}\mathrm{on}8:00$$$$5+5+5+5+5+5+4+3+2+1=40$$

Commented by chux last updated on 14/Jun/17

$$\mathrm{i}\mathrm{really}\mathrm{appreciate}\mathrm{this}$$

Answered by ajfour last updated on 14/Jun/17

Commented by RasheedSoomro last updated on 14/Jun/17

$$\mathrm{I}\mathrm{always}\mathrm{appreciate}\mathrm{your}\mathrm{skills}\mathrm{to}$$$$\mathrm{draw}\mathrm{diagrams}!$$$$(\mathrm{And}\mathrm{of}\mathrm{course}\mathrm{geometrical}\mathrm{skills}\mathrm{\&}$$$$\mathrm{knowledge}\mathrm{too}!)$$$$\mathrm{Good}\mathrm{luck}\mathrm{my}\mathrm{friend}!$$

Commented by ajfour last updated on 14/Jun/17

$$thanksalotSir,pleaseviewmy$$$$solutiontoQ.15828..icould$$$$provethatmainlybecausei$$$$extrapolatedthemedians$$$$of\mathrm{\Delta }ABC.$$

Answered by mrW1 last updated on 14/Jun/17

$$\mathrm{each}\mathrm{man}\mathrm{can}\mathrm{do}\mathrm{each}\mathrm{hour}\frac{1}{5\times 8}=\frac{1}{40}$$$$10:00\mathrm{am}-4:00\mathrm{pm}:$$$$\mathrm{work}\mathrm{done}=5\times 6\times \frac{1}{40}=\frac{3}{4},\mathrm{rest}=1-\frac{3}{4}=\frac{1}{4}$$$$4:00\mathrm{pm}-5:00\mathrm{pm}:$$$$\mathrm{work}\mathrm{done}=4\times 1\times \frac{1}{40}=\frac{1}{10},\mathrm{rest}=\frac{1}{4}-\frac{1}{10}=\frac{3}{20}$$$$5:00\mathrm{pm}-6:00\mathrm{pm}:$$$$\mathrm{work}\mathrm{done}=3\times 1\times \frac{1}{40}=\frac{3}{40},\mathrm{rest}=\frac{3}{20}-\frac{3}{40}=\frac{3}{40}$$$$6:00\mathrm{pm}-7:00\mathrm{pm}:$$$$\mathrm{work}\mathrm{done}=2\times 1\times \frac{1}{40}=\frac{1}{20},\mathrm{rest}=\frac{3}{40}-\frac{1}{20}=\frac{1}{40}$$$$7:00\mathrm{pm}-8:00\mathrm{pm}:$$$$\mathrm{work}\mathrm{done}=1\times 1\times \frac{1}{40}=\frac{1}{40},\mathrm{rest}=\frac{1}{40}-\frac{1}{40}=0$$$$\Rightarrow \mathrm{at}8:00\mathrm{pm}\mathrm{the}\mathrm{work}\mathrm{is}\mathrm{completely}\mathrm{done}.$$$$\Rightarrow \mathrm{answer}\left(\mathrm{d}\right)$$

Commented by chux last updated on 14/Jun/17

$$\mathrm{I}\mathrm{must}$$$$\mathrm{confess}{\mathrm{I}}^{\prime }\mathrm{ve}\mathrm{learnt}\mathrm{so}\mathrm{much}\mathrm{from}$$$$\mathrm{you}.\mathrm{Thank}\mathrm{you}\mathrm{so}\mathrm{much}.$$$$$$

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