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03 Aug 2011, 22:09
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D
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Difficulty:
85%
(hard)
Question Stats:
57% (03:08) correct
43%
(03:40)
wrong
based on 191
sessions
History
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A dye company received an order of 400 litres of black dye and 360 litres of brown dye. It has two machines (X and Y) to make these dyes. X takes 4 hours to make 16 litres of black dye and 3 hours to make 9 litres of brown dye. Y takes 4 hours to make 12 litres of black dye and 3 hours to make 12 litres of brown dye. If the company has to deliver the order in 93 hours, its delivery will be delayed by at least
(1) 2.5 hrs
(2) 2 2/7 hrs
(3) 2 4/7 hrs
(4) 2 5/7 hrs
gma.jpg [ 26.3 KiB | Viewed 9294 times ]
(1) 2.5 hrs
(2) 2 2/7 hrs
(3) 2 4/7 hrs
(4) 2 5/7 hrs
Attachment:
gma.jpg [ 26.3 KiB | Viewed 9294 times ]
03 Aug 2011, 23:03
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X can make 4 L/hr of black dye but only 3 L/hr of brown dye.
Y can make 4 L/hr of brown dye but only 3 L/hr of black dye.
Therefore let X make the black dye and Y make the brown dye.
In 93 hours, X would have made 93*4 = 372 L of black dye.
In 90 hours, Y would have made 90*4 = 360 L of brown dye. For the next 3 hours, it can make black dye as the brown dye is done.
So in 93 hours, total amount of black dye made = 372 L + 3*3 L = 381 L of black dye.
Amount of black dye remaining = 19 L
Rate of production of black dye = 3 L/hr (Y) + 4 L/hr (X) [as both are working on producing black dye now] = 7 L /hr
Amount of extra time required = 19/7 hours = 2 5/7 hours
Option (4) [or (D) in the usual form] is correct.
Y can make 4 L/hr of brown dye but only 3 L/hr of black dye.
Therefore let X make the black dye and Y make the brown dye.
In 93 hours, X would have made 93*4 = 372 L of black dye.
In 90 hours, Y would have made 90*4 = 360 L of brown dye. For the next 3 hours, it can make black dye as the brown dye is done.
So in 93 hours, total amount of black dye made = 372 L + 3*3 L = 381 L of black dye.
Amount of black dye remaining = 19 L
Rate of production of black dye = 3 L/hr (Y) + 4 L/hr (X) [as both are working on producing black dye now] = 7 L /hr
Amount of extra time required = 19/7 hours = 2 5/7 hours
Option (4) [or (D) in the usual form] is correct.
General Discussion
04 Aug 2011, 05:09
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the maximum work will be when x deals with black and y with broun.
in 90 minutes y completes its work (360) and x completes 360 from 400.
so only 40 black are left. in common they complete 7 black.
so 40/7=5 and 5/7. together its 90+ 5 and 5/7-93
in 90 minutes y completes its work (360) and x completes 360 from 400.
so only 40 black are left. in common they complete 7 black.
so 40/7=5 and 5/7. together its 90+ 5 and 5/7-93
