P can complete a piece of work in 16 days,whi | vedclass

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Question

(B) Let the total work be the $LCM$ of $16$ and $32$,which is $32$ units.
Efficiency of $P = 32 / 16 = 2$ units/day.
Efficiency of $Q = 32 / 32 = 1$

Vedclass · Accepted Answer

Quantity $I < $ Quantity $II$

Vedclass · Answer

(B) Let the total work be the $LCM$ of $16$ and $32$,which is $32$ units.
Efficiency of $P = 32 / 16 = 2$ units/day.
Efficiency of $Q = 32 / 32 = 1$ unit/day.
Quantity $I$ ($P$ starts first):
Day $1$: $P$ does $2$ units. Day $2$: $Q$ does $1$ unit. Total $3$ units in $2$ days.
In $20$ days ($10$ cycles),$30$ units are completed.
On the $21$st day,$P$ does $2$ units. Total work $32$ units completed in $21$ days.
Quantity $II$ ($Q$ starts first):
Day $1$: $Q$ does $1$ unit. Day $2$: $P$ does $2$ units. Total $3$ units in $2$ days.
In $20$ days ($10$ cycles),$30$ units are completed.
On the $21$st day,$Q$ does $1$ unit. Remaining work $32 - 31 = 1$ unit.
$P$ completes the remaining $1$ unit in $1/2$ day.
Total time $= 21.5$ days.
Since $21 < 21.5$,Quantity $I < $ Quantity $II$.

$P$ can complete a piece of work in $16$ days,which $Q$ can complete in $32$ days. If $P$ and $Q$ work on alternate days,find the relationship between Quantity $I$ (Total days taken if $P$ starts) and Quantity $II$ (Total days taken if $Q$ starts).

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