1. Calculate the total hours worked by consultants P and Q.
2. Calculate the total amount paid to each consultant.
3. Deduct the total amount paid to both consultants from the client's budget to find the remaining amount.
Let's start with the first step:
1. Total hours worked by consultant P:
The hour hand of a clock completes 360 degrees in 12 hours, so 210 degrees correspond to (210/360) * 12 hours = 7 hours.
However, consultant P took two tea breaks of 15 minutes each, totaling 30 minutes or 0.5 hours.
So, the actual hours worked by consultant P = 7 hours - 0.5 hours = 6.5 hours.
Total hours worked by consultant Q:
Similar to P, 240 degrees correspond to (240/360) * 12 hours = 8 hours.
But Q took a lunch break of 20 minutes or 1/3 hours.
So, the actual hours worked by consultant Q = 8 hours - 1/3 hours = 7.67 hours (rounded to two decimal places)
2. Calculate the total amount paid to each consultant:
Consultant P: 6.5 hours * $200/hour = $1300
Consultant Q: 7.67 hours * $200/hour = $1534
3. Deduct the total amount paid to both consultants from the client's budget:
Total amount paid to consultants = $1300 + $1534 = $2834
Remaining amount for the client = $3000 - $2834 = $166
So, after paying the consultants, the client shall have USD 166 remaining.