GATE ECE 2019 | GA | Question: 9

Question

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.

• A. $000.00$
• B. $166.67$
• C. $300.00$
• D. $433.33$

Answer 1

$360^{\circ}$ 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. 

Correct Answer: B.

Answer 2

$P\&Q\ Started:8AM$

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

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$:B$

Answer 3

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.

Answer 4

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