The second worker did not produce 16 parts in 8 hours, which means it will produce more than 2 parts every hour. Secondly, the 5 minutes is the time difference in producing one part between first and second worker so it could not be that 2 parts are produced in 5 minutes every hour. Did I miss something please?

Let the 2nd worker takes x hrs to complete one part , a/c to ques 1st worker will take ( x + 5/60) = ( x + 1/12) hrs to complete one part.

So in 1 hr 2nd worker completes 1/x parts
and in 1 hr 1st worker completes 1/ ( x + 1/12) parts

According to the question in 8 hrs the 2nd workers produces 16 more parts than 1st worker.

So in 8 hrs 2nd worker completes 8* (1/x) parts ----- A
And in 8 hrs 1st worker completes 8 * ( x + 1/12) parts .------ B

According to the question 8/x parts = 8/ ( x + 1/12) + 16

after solving we get the following quadratic equation
24 *x square + 2*x - 1 =0

Solving the above quadratic equation we get x = 1/6 and x = -1/4
since x can not be negative so 1/x can not be negative . so x = 1/6.

Now we have to find total parts produced by both workers in 8 hrs , which shall be adding A and B.

we get 8/1/6 + 8/ ( x + 1/12) , solving we get value as 48 + 32 = 80.

Should not the answer be 80. What am I missing here. Need help !!

Worker 1: creates 1 part in (x+5) mins. So, 1/(x+5) parts is created in 1 min. This means 480/(x+5) parts in 8 hrs.
Worker 2: creates 1 part in x mins. So, 1/x parts is created in 1 min. This means 480/x parts in 8 hrs.

(480/x)-(480/(x+5))=16
x=10
In 16 hrs, worker 1 creates 32 parts and worker 2 creates 48 parts. Total: 80.
What am I missing here? Carcass

Let the number made by slower worker be x, so the more productive worker makes x+16.

Time taken by both is 8 hrs or 480 minutes.

The difference in their time to make one unit is 5 minutes => \(\frac{480}{x}-\frac{480}{x+16}=5\)

\(480(x+16)-480(x)=5(x)(x+16)\)

\(96*16=x^2+16x\)

\(x^2+16x-48*32=0\)

\((x+48)(x-32)=0\)

So x can be 32 or -48, but x cannot be negative.

Based on your solution, if x=32,

That means the total parts made by both workers is 32+16 =48.

Infact the same thing pointed out by chetan2u in his solution

https://gmatclub.com/forum/two-workers- ... l#p2799927

the stated solution to this question is incorrect. the correct answer for many parts they make together is 80. if you want 32 to be the correct answer, then the question should ask how many parts the slower worker makes in 8 hours

Yes You are correct sir