Question
The painting of a hotel can be done by 10 painters in 5 days. But, in reality there were few dabblers in the group of 10 painters and therefore the work took a little over 6 days for completion. A painter worked twice as fast as the dabbler and used 25% less paint than a dabbler used. If 5 litres extra paint was used than expected, then the total paint used in painting the hotel was (in litres)
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Answer:
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Option (d)
Let the number of painters be x, then dabblers is 10 - x
Now x50+(10−x)100= slightly less than 12
(2x+10−x)100= slightly less than 16
x+10 = slightly less than 1006
x= slightly less than 6.67
Since x has to be integer nearest integer is 6.
That means the number of dabblers = 4.
Let p be the amount of paint used by each dabbler, so by each painter = .75p
Extra paint used =.25p×4= 5 litres
So p = 5 litres.
Dabblers will be using 5×4 = 20 litres of paint. Now as the painters are working at twice the efficiency, they will use twice the amount of 75% of paint used by dabbler in the same time.
i.e. paint used by each painter =2×(.75)×5 = 7.5 litres.
Hence paint used by 6 painters =7.5×6= 45 litres
So total paint used = 45 + 20 = 65litres
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:
Option (d)
Let the number of painters be x, then dabblers is 10 - x
Now x50+(10−x)100= slightly less than 12
(2x+10−x)100= slightly less than 16
x+10 = slightly less than 1006
x= slightly less than 6.67
Since x has to be integer nearest integer is 6.
That means the number of dabblers = 4.
Let p be the amount of paint used by each dabbler, so by each painter = .75p
Extra paint used =.25p×4= 5 litres
So p = 5 litres.
Dabblers will be using 5×4 = 20 litres of paint. Now as the painters are working at twice the efficiency, they will use twice the amount of 75% of paint used by dabbler in the same time.
i.e. paint used by each painter =2×(.75)×5 = 7.5 litres.
Hence paint used by 6 painters =7.5×6= 45 litres
So total paint used = 45 + 20 = 65litres
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