Machine A produces parts twice as fast as machine B does. Machine B pr

1. Find rates of Machines B and A in hours.

Machine B rate: B makes 100 parts in 40 minutes. 40 minutes is \(\frac{2}{3}\) of one hour.

B's rate = \(\frac{100}{(\frac{2}{3})}\) =

\(\frac{100}{1} * \frac{3}{2}\) =

\(\frac{300}{2}\) or 150 parts in 1 hour. B = \(\frac{150}{1}\)

A's rate for product X: A produces parts twice as fast as B does.

In one hour Machine A will produce \(\frac{150}{1}\) * 2 = 300 parts of product X in 1 hour --> \(\frac{300}{1}\)

2. Find rate of Machine A for product Y.

To produce each part of Y takes \(\frac{3}{2}\) times as long as it does to produce each part of product X.

Machine A produces 300 parts in one hour for product X. \(\frac{3}{2}\) times as long means 1.5 hours for the same amount of parts.

A's rate for product Y is \(\frac{300}{1.5} = \frac{3000}{15}\) = 200 Y parts in one hour =\(\frac{200}{1}\)

3. Find how many parts of Product Y that Machine A can make in 6 minutes.

Time in hours: \(\frac{6 min}{60 min}\) = \(\frac{1}{10}\) hour

A's rate for producing Y is \(\frac{200}{1}\) parts per hour

R*T = W --- >\(\frac{200}{1}\) * \(\frac{1}{10}\) = 20 parts

Answer D

B's rate = 100 of X parts / 40 mints =100/40

thus A's rate = 2*100/40= 200/40 = 1/5
i.e A can produce 1 of x product in 5 minutes..

now we have product Y which takes 3/2 of time it takes to produce product X

so now A will take 1/5 *3/2 = 3/10 minutes to produce 1 of Y product
A's rate = 10/3
with similar rate if A works for 6 minutes , A produces = 10*6/3 = 20 products of Y

Ans D

100 products of X in 40 min for Machine B
200 Products of X in 40 min for Machine A (because machine A has double the speed of B)
200/40 = 5 products of X a min for Machine A
In 6 min - 30 products of X
For Y - It takes 50% extra time (3/2 in percentage terms is 50% extra), which means productivity will reduce by 33.33% (which is 1/3 in fractional form)
So, Machine A, which could make 30 products of X and now make only 20 products of Y (1/3rd reduction in productivity)

Given in the question
Machine A produces parts twice as fast as machine B does
AND
Machine B produces 100 parts of product X in 40 minutes
so according to the question
Machine A produces 100 parts of product X in 20 minutes

Also given in the question..
each part of product Y takes 3/2 times of the time taken to produce each part of product X

so
Machine A produces 100 parts of product Y in 20x3/2 minutes i.e 30minutes
so. if in 30 mins Machine A produces 100 parts of product Y
then in 6 minutes Machine A will produce 100x6/30 parts of product Y i.e 20 parts of product Y D

Since each part of Y takes 3/2 as long as each part of X -- and B takes 40 minutes to produce 100 parts of X -- the time for B to produce 100 parts of Y = \(\frac{3}{2} * 40 = 60\) minutes.
Since A is twice as fast as B -- and B produces 100 parts of Y in 60 minutes -- A produces 200 parts of Y in 60 minutes.
Since in 60 minutes A produces 200 parts of Y, in 6 minutes A produces 20 parts of Y.

machine B produces 100 parts in 40 mins
given A machine produces parts twice as fast as B ; so in 20 mins A produces 100 parts
time for Y product for machine A ; 20*3/2 ; 30 mins
so rate ; 100/30
and 6 mins A will produce ; 100/30 * 6 ; 20 IMO D

Speed of Machine A = 2 * Speed of Machine B.

M/c B: 100 parts take time = 40 minutes
1 part take time = \(\frac{40}{100}\) minutes = \(\frac{2}{5}\) minutes

Since product Y takes 3/2 times of time taken to produce each part of product X by M/c B, time taken to produce 1 part of product Y by M/c A = \(\frac{3}{2}\) * \(\frac{2}{5} = \frac{3}{5}\) minutes

Now in \(\frac{3}{5}\) minutes parts of product Y produced by M/c A with speed of M/c B = 1 part.
Similarly, in 1 minute parts of product Y produced by M/c A with speed of M/c B = \(\frac{5}{3}\) parts
Hence in 6 minutes parts of product Y produced by M/c A with speed of M/c B = \(\frac{5}{3} * 6\) = 10 parts

As speed of M/c A is twice that of M/c B parts produced in twice the speed of M/c B = 10 * 2 = 20 parts

Answer D.

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