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28 Jun 2024, 01:30
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Each type P machine can assemble 240 cars per hour, each type Q machine can assemble 360 cars per hour, and each type R machine can paint 1500 cars per hour. Any car is painted only when it is completed assembled. Find out, for a particular hour, what is the total number of machines working?
(1) A total of 6,000 cars are assembled and painted every hour.
(2) For that one hour, there are 5 Type Q machines working for every 2 Type R machine working.
(1) A total of 6,000 cars are assembled and painted every hour.
(2) For that one hour, there are 5 Type Q machines working for every 2 Type R machine working.
28 Jun 2024, 02:40
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Assemble
P : 240 cars/hr having p machine(s)
Q : 360 cars/hr having q machine(s)
Paint
R : 1500 cars/hr having r machine(s)
hence, assemble 240p + 360q cars/hour and paint 1500 r cars/hour
(1) 6000 cars were assembles & paint
Assemble eq. : 240p + 360q = 6000 ---> 2p+3q = 25 Insufficient
Paint eq. : 1500r = 6000 ---> r = 4
(2) q/5 = r/2 Insufficient
(1+2) we know from (1) that r = 4 and (2) that q/5 = r/2, that mean q = 10
from Assemble eq. : 240p + 360q = 6000 and q = 10 , so, p = 10 sufficient
P : 240 cars/hr having p machine(s)
Q : 360 cars/hr having q machine(s)
Paint
R : 1500 cars/hr having r machine(s)
hence, assemble 240p + 360q cars/hour and paint 1500 r cars/hour
(1) 6000 cars were assembles & paint
Assemble eq. : 240p + 360q = 6000 ---> 2p+3q = 25 Insufficient
Paint eq. : 1500r = 6000 ---> r = 4
(2) q/5 = r/2 Insufficient
(1+2) we know from (1) that r = 4 and (2) that q/5 = r/2, that mean q = 10
from Assemble eq. : 240p + 360q = 6000 and q = 10 , so, p = 10 sufficient
Given - Each type P machine can assemble 240 cars per hour, each type Q machine can assemble 360 cars per hour, and each type R machine can paint 1500 cars per hour.
Assuming no of P machines as p, similarly for q for Q and r for R.
Find out, for a particular hour, what is the total number of machines working?
1st - A total of 6,000 cars are assembled and painted every hour.
Threfore 240p + 360q = 6000 and 1500r = 6000
on simplification 2p + 3q = 50 and r = 4
There are 8 possible non zero values for (p,q) .. Not sufficient.
2nd - For that one hour, there are 5 Type Q machines working for every 2 Type R machine working.
Therefore ratio q/r = 5/2 Cant say anything hence not sufficient.
Combining both we know r = 4 So q=10
2p + 3q = 50 put q=10
2p = 20, p=10. Total machines p+q+r = 10+10+4=24.
Answer C.
Assuming no of P machines as p, similarly for q for Q and r for R.
Find out, for a particular hour, what is the total number of machines working?
1st - A total of 6,000 cars are assembled and painted every hour.
Threfore 240p + 360q = 6000 and 1500r = 6000
on simplification 2p + 3q = 50 and r = 4
There are 8 possible non zero values for (p,q) .. Not sufficient.
2nd - For that one hour, there are 5 Type Q machines working for every 2 Type R machine working.
Therefore ratio q/r = 5/2 Cant say anything hence not sufficient.
Combining both we know r = 4 So q=10
2p + 3q = 50 put q=10
2p = 20, p=10. Total machines p+q+r = 10+10+4=24.
Answer C.
