Dewgmat wrote:

The perimeter of a square is equal to the perimeter of a rectangle. The length of the rectangle is three times longer than is width having total area of 1200 sq.meter. What will be the total cost if the total area of the square is covered with stones having a dimension of 50 cm.sq. each and if Rs. 50 is charged for placing a stone in the square?

Find the perimeter of the rectangle using area; then find perimeter and area of square; convert area of square into square centimeters (we have meters); and find total cost for placing some number of stones on the larger square.

1) Perimeter of rectangle

Area of rectangle, where length is three times longer than width, x = width :

\(3x * x = 1,200\)

\(3(x^2) = 1,200\)

\(x^2 = 400\)

\(x = 20\)

Rectangle length = 3x = 60m

Rectangle width = x = 20m

Rectangle perimeter = 2L + 2W = 160m

2) Perimeter and area of square, and convert to square centimeters

Perimeter of rectangle =

Perimeter of square, where

s = side of square

160 m = 4s

s = 40 m

We need big square's area in sq cm.

Side = 40m * 100cm/1m = 4,000cm

Area = \(4,000^2 = 16 * 10^6\) sq cm

3) Total cost

We could stop here. We need to divide large square area by the area of smaller squares to see how many will fit, but then we will multiply by a unit cost that is exactly equal in value to the area, in sq cm, of the little squares.

In other words, we will divide by 50 for the area to get the number of tiles, and then multiply by 50 to get the cost of that many tiles.

The cost, therefore, is the total area in rupees -- because (* 50) then (/ 50) brings us back to original.

TOTAL COST

Rs. 16,000,000 If you had not noticed that shortcut, you could rewrite area as

\(1600 * 10^4\) sq cm (to divide by 50 easily)

\(\frac{(1600 * 10^{4})}{50} = 32 * 10^4\) = number of smaller squares that will fit in larger square

If it costs Rs. 50 to put a stone on each small square, then the total cost is

(Rs. 50)(32)(10\(^4\))

From above we know (32 * 50 = 1600), so total cost is Rs. 1600 * 10\(^4\), or

Rs. 16,000,000

A few questions:

1) Do you have answer choices so that this question is more like the real GMAT?

2) What is the source of this question?

3) What is the answer and/or does anyone see a mistake in my calculations?

4) Is there a shorter way to do this problem? I don't think so. Just checking.

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