A company uses 2 machines to fill an order for 3,360 bottle caps.

I have calculated that D is the correct answer. I took a convntional approach of calculating the production per hour for each machine and found out that after two cycles of production and repair 3360 caps would have produced and that machine B would have contributed 8 (2 cycles * 4 h/cycle) * 240 (caps/hour) = 1920 caps. After the 8 hour timeframe machine B would stop for maintenance, but machine A would keep working for 1 more hour, because it requires one hour longer maintenance, totaling also 8 hours of work. So, its contribution would be 8 * 180 = 1640. And the total production in 9 hours would be 3360.

For Machine A:
72 Caps in 24 min; 1 min -> 72/24 Caps; 1 Hour -> 72*60/24 = 180 Caps:

For Machine B:
48 Caps in 12 min; 1 min -> 48/12 Caps; 1 Hour -> 48*60/12 = 240 Caps:

Combined Output in One Hour (A+B): 420 Caps

At starting both can work for 4 hours: Output= 420*4 = 1680

Remaining: 3360-1680 = 1680 (Both working together will require 4 hours as previous)

Now, A will be Calibrated for 3 hours, and B will Calibrated for 2 Hours;

After calibration B will have to work for 4 Hours to complete the work;

So the caps made by B would be: 240 * 8 = 1920

I dont get it so machine b will sit on its hutt and not work a extra hour until a is fixed where is this mentioned? all calculations are wrong otherwise.

If both machines begin working at the same time, and are working whenever they are not being recalibrated

this is what is mentioned in the question. And I assume u are aware of the machines A and B have different recalibration hours - 3 hrs and 2 hrs respectively. And both work for 4 hrs continuously, with the difference being their hours of idle state (recalibrating time). So B starts to work the third hour , when A was idle.

Hope this answers ur doubt.

I would suggest u to take a look at the most favourable reply.

Machine A produce 72 caps in 24 min -- rate is 3caps /min and works for 4 hours before recalibration means in 4 hours A produce 3*4*60 =720 caps before a 3-hour recalibration

Machine B produces 48 caps in every 12 mins --- rate is 4 caps/min then works for 4hours means it produces in 4 hours 4*4*60= 960 caps before a 2-hour recalibration

Both starts working together

Time; 0--1--2--3--4--5--6--7--8--9--10--11--12--13--14--15

mA /------720---/-stop---/-------720----/--stop------/----720----
mB /-----960----/--stop/-----960----/--stop--/---960-----------

A+B /----1680---/---stop/----3360--------/

both start together after 4 hours they produce 1680 then recalibration for them. B will start 1 hour early than A and will produce 240 the total will be 1920 before A join and they work together for 3 hours from 7 to 10 to add (3*60+4*60) *3hours =420*3=1260 for the total to be 3180 and A will continuous 1 hour alone to produce 3*60=180 during this time with B already started it second recalibration to complete the 3360 needed.

total produce by mB is 960*2= 1920 caps