arun8sharma wrote:
Hey,
Please help me out.
A 12 d for 2 shifts so for 1.5 shifts, it is 9 d
B 15 d for 2 shifts so for 1.5 shifts it is 15/4 d
How to move from here? I am stuck and unable to understand how to move forward?
Hi, you must first calculate how many days it takes each machine working just ONE shift:
Machine A: If it takes 12 days working 2 shifts per day, then it takes 24 days working 1 shift per day.
Machine B: If it takes 15 days working 2 shifts per day, then it takes 30 days working 1 shift per day.
We are told that each machine is going to be working 1.5 shifts each day, which is 3/2 as a fraction, therefore:
Rate of Machine A + Rate of Machine B = [(3/2)/24] + [(3/2)/30]
The least common denominator of 24 & 30 is 120
{[(3/2)/24]x(5/5)} + {[(3/2)/30]x(4/4)} = [(15/2)/120] + (6/120) = [(15/2)+6]/120
Let's solve the numerator:
(15/2) + (6/1) = (15/2) + (12/2) = 27/2
Plug the numerator back into the equation:
(27/2)/120 = (27/2)/(120/1) = (27/2)x(1/120) = (9/2)x(1/40) = 9/80
Therefore, each machine working 1.5 shifts would complete 9 jobs in 80 days
But we want to know how many days it would take to complete just 1 job at this rate, so we need to divide 80 by 9
80/9 = 8.88 which is roughly 9 days
The correct answer is choice (D)