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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. $433.33$

For P :  hour hand moved by  $210^{\circ}$. So the hour hand will cover the distance equivalent to  $\frac{210^{\circ}\times 12}{360^{\circ}}= 7hr$

For Q:  hour hand moved by  $210^{\circ}$. So the hour hand will cover the distance equivalent to  $\frac{240^{\circ}\times 12}{360^{\circ}}= 8hr$

Effective work hours for P :  $7-(0.25\times 2)=6.5$

Effective work hours for Q:  $8-0.334=7.667$

Total bill for the consultants :  $(6.5\times200)+(7.667\times200)=2833.4$

Amount remaining with the client:  $3000-2833.4=166.67$

Option B is correct
960 points