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Two design consultants, $P$ and $Q,$ started working from $8$ AM for a client. The client budgeted a total of USD $3000$ for the consultants. $P$ stopped working when the hour hand moved by $210$ degrees on the clock. $Q$ stopped working when the hour hand moved by $240$ degrees. $P$ took two tea breaks of $15$ minutes each during her shift, but took no lunch break. $Q$ took only one lunch break for $20$ minutes, but no tea breaks. The market rate for consultants is USD $200$ per hour and breaks are not paid. After paying the consultants, the client shall have USD _______ remaining in the budget.

1. $000.00$
2. $166.67$
3. $300.00$
4. $433.33$
Migrated from GO Electronics 3 years ago by Arjun

$360^{\circ}$ is covered in $12$ hours by a hour hand of a clock.

"P stopped working when the hour hand moved by $210$ degrees on the clock. Q stopped working when the hour hand moved by $240$ degrees."

It means $P$ stopped working after $\frac{210^{\circ}}{360^{\circ}}*12 = 7$ hours and $Q$ stopped working after $\frac{240^{\circ}}{360^{\circ}}*12 = 8$ hours.

-- Since, $P$ has taken $2$ tea breaks of total $30$ minutes, $P$ has worked for total $(7 -0.5) = 6.5$ hours

-- Since, $Q$ has taken one lunch break of total $20$ minutes, $Q$ has worked for total $7\;hours\; and\; 40\; minute=(7+\frac{40}{60})= (7 + 0.6667)\; hours = 7.6667$ hours

So, $P$ and $Q$ are paid total USD $(6.5+7.6667)*200 =2834.33$

So, after paying the consultants, the client shall have USD $(3000 - 2834.33) =166.67$ remaining in the budget.

$P\&Q\ Started:8AM$

$P:210^{\circ}\Rightarrow3PM \Rightarrow7hours$

P took two tea breaks of 15 minutes each during her shift

Working hours$=6:30$

$(6h\times 200)\$+100\$=1300\$$Q:240^{\circ}\Rightarrow4PM \Rightarrow8hours Q took only one lunch break for 20 minutes Working hours=7:40 (7h\times 200)\+133.\bar3\=1533.\bar3\$$ After paying the consultants, the client shall have USD _______ remaining in the budget.$3000\$-2833.\bar3\$=166.67\

Correct Answer$:B$