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 1

Option (d)
Let the number of painters be x, then dabblers is 10 - x
Now $\frac{x}{50}+\frac{(10-x)}{100}$= slightly less than $\frac{1}{2}$
$\frac{(2x+10-x)}{100}$= slightly less than $\frac{1}{6}$
x+10 = slightly less than $\frac{100}{6}$
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 =$.25p\times 4$= 5 litres
So p = 5 litres.
Dabblers will be using $5\times 4$ = 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 =$2\times \left(.75\right)\times 5$ = 7.5 litres.
Hence paint used by 6 painters =$7.5\times 6$= 45 litres

So total paint used = 45 + 20 = 65litres