Problem Solving

Can anybody help me get the answer to this question.
I guess I need to get the language translation for this question,

If Machine A works for 80 minutes to produce X and has a productivity ratio of 4:5 to Machine B, how long does machine B take to produce X

manihar.sidharth wrote:Can anybody help me get the answer to this question.
I guess I need to get the language translation for this question,

If Machine A works for 80 minutes to produce X and has a productivity ratio of 4:5 to Machine B, how long does machine B take to produce X

Do not worry about this wording.
The GMAT will not use the term productivity ratio.

That said, the red portion implies the following:
(A's rate)/(B's rate) = 4/5.
In other words:
In the time it takes A to produce 4 widgets, B can produce 5 widgets.

Since rate and time are RECIPROCALS, we get:
(A's time)/(B's time) = 5/4.

Thus:
B's time = (4/5)(A's time) = (4/5)(80) = 64 minutes.

A's rate = X/80

lets B's rate is X/T

A's rate/B's rate = 4/5

X/80 /(X/T) = 4/5

(X/80) * (T/X) 4/5

T = 4* 80/5 = 64

B takes 64 minutes

Since rate and time are RECIPROCALS, we get:
(A's time)/(B's time) = 5/4.

Hi Mitch ,

Can you please explain why Reciprocal ?

I Don't understand the above part.

Many thanks in advance.

SJ

Hi ,

Please reply on my query.

Many thanks in advance.

SJ

jain2016 wrote:

Since rate and time are RECIPROCALS, we get:
(A's time)/(B's time) = 5/4.

Hi Mitch ,

Can you please explain why Reciprocal ?

I Don't understand the above part.

Many thanks in advance.

SJ

Rate the time have a RECIPROCAL relationship.

If A works 3 times as fast as B, then A's time will be 1/3 B's time.
To illustrate:
Let A's rate = 3 widgets per hour and B's rate = 1 widget per hour, with the result that A works 3 times as fast as B.
Time for A to produce 3 widgets = w/r = 3/3 = 1 hour.
Time for B to produce 3 widgets = w/r = 3/1 = 3 hours.
Result:
A's time (1 hour) is equal to 1/3 B's time (3 hours).

If A's time is 1/2 B's time, then A works twice as fast as B.
To illustrate:
Let A's time to produce 2 widgets = 1 hour and B's time to produce 2 widgets = 2 hours, with the result that A's time is 1/2 B's time.
A's rate = w/t = 2/1 = 2 widgets per hour.
B's rate = w/t = 2/2 = 1 widget per hour.
Result:
A's rate (2 widgets per hour) is twice B's rate (1 widget per hour).

In the problem posted above, (A's rate)/(B's rate) = 4/5.
Thus, (A's time)/(B's time) = 5/4.