If it takes two hours for 3 machines to paint four rooms

Question

If it takes two hours for 3 machines to paint four rooms, how many hours will it take 10 machines to paint twenty rooms?​

A. 2​
B. 3​
C. 4​
D. 10​
E. 20​

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yashikaaggarwal · Answer

two hours for 3 machines to paint four rooms
1 machine takes 2 hours to complete 4/3 room
1 machine take 1 hour to complete 4/6 room.

10 machine will take 1 hour to complete = 4*10/6 = 20/3 = 6.66 room --------------------(1)
10 machine will take x hours to complete 20 rooms ----------------(2)
equating both,
X = 20/6.66
X = 3

Answer is B

GMATinsight · Answer

CONCEPT :  \frac{M*T}{W} = COnstant

i.e.  \frac{3*2}{4} = \frac{10*T}{20}

i.e.  T = 3

ANswer: Option B

EgmatQuantExpert · Answer

Given

• It takes two hours for 3 machines to paint four rooms

To Find

• The number of hours for 10 machines to paint twenty rooms.

Approach and Working Out

• Four rooms need 2 hours for 3 machines.
• Four rooms need 6 hours in total.
• 20 rooms will require  \frac{(20 × 6)}{4} 
 =30 hours 
• 10 machines would need  \frac{30}{10} 
 = 3 hours

Correct Answer: Option B

sam67 · Answer

4 rooms= 1 work; 20 rooms= 5x work

Now,
3 Machines ->2 hours -> 4 rooms 
1 Machine -> 6 (i.e. 2*3) hours 
10 Machines -> 6/10 hours for 1 work (i.e. 4 rooms)

For 20 rooms (i.e. 5x work)
10 machines would need 6/10*5= 3 hours

The answer is B.

Nipungupta9081 · Answer

Answer is B

it takes two hours for 3 machines to paint four rooms 
Putting the values in R*T = W table = 3 * 2 = 4 -------- ( 1 )
 
10 machines to paint twenty rooms , how many hours = 10 * T = 20 ------ ( 2 )

3*2/ 4 = 10 * T / 20
T = 3

ashmitakhan · Answer

Is my approach correct?
3 machines take 2 hours: So, W=r*t
rate for 1 machine= M
rate of 3 machines= 3M
Units of work done= 3M*2= 6M

Now, 6M of work is done on 4 rooms. So, work done on one room?
1 room= 6M/4
So, work done on 20 rooms is 3M/2*20= 30M

We know, w=r*t
30M= 10M*t 
t= 3hours

LukeShaw · Answer

two hours for 3 machines to paint four rooms

machine speed = 4/(2*3) room/hour/machine

10 machines to paint twenty rooms?

Given unchanged machine speed,

4/6 room/machine/hour* 10 machines * time = 20 rooms

time = 3 hours

The answer is B

MathRevolution · Answer

\frac{{M_1 * D_1 * H_1} }{ {W_1}}  =  \frac{{M_2 * D_2 * H_2} }{ {W_2}}

=>  \frac{{3 * 2} }{ {4}}  =  \frac{{10 * H_2} }{ {20}}

=>  H_2  =  \frac{{3 * 2 * 20} }{ {4 * 10}}

=>  H_2  = 3 hours

Answer B

e3thekid · Answer

Rate (3 machines) : 
4 rooms / 2 hours —> 2 rooms / 1 hour

Rate (1 machine) : 
Rate (3 machines) / 3 = (2 / 1) / (3) = 2 rooms / 3 hours

Rate ( 10 machines) :
Rate (1 machine) x 10 = (2 / 3) (10) = 20 rooms / 3 hours

t = 3 hours

Option B

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If it takes two hours for 3 machines to paint four rooms

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If it takes two hours for 3 machines to paint four rooms

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