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lots of calculation!! is there a better way?

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by AJWILL » Sat Aug 04, 2012 11:49 am
A labourer lays marble tiles in a rectangular plot of length 990 ft and breadth 396 ft. If he charges $45 per acre to lay the tiles. What is the total cost of laying the tiles in the plot? (43,560 square feet = 1 acre
[A] $400
$405
[C] $410
[D] $360
[E] $450
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by eagleeye » Sat Aug 04, 2012 12:49 pm
AJWILL wrote:A labourer lays marble tiles in a rectangular plot of length 990 ft and breadth 396 ft. If he charges $45 per acre to lay the tiles. What is the total cost of laying the tiles in the plot? (43,560 square feet = 1 acre
[A] $400
$405
[C] $410
[D] $360
[E] $450


Since the numbers are pretty close, I can't think of a faster way than calculating. However, we can try to do the minimum amount of calculations.
We know that area of plot = 990*396. Keep it as such.

Now cost of laying tiles = 45*990*396/43560 =
45* 99*396/4356 = 5*9*11*9*4*11*9/(4356). Now 4356 is divisible by 4 because its last two digits (56) are divisible by 4. The 4 at the top will cancel out. We will be left with all odd integers on the denominator.

Hence, looking at the answer choices we know that only B can be the answer since the denominator will be odd, making the integer answer odd. 405 is the only odd answer.

Hence we choose B without doing much calculation.
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