CONSTRUCTION | Estimates | 5 Questions (EASY-MODERATE)

CONSTRUCTION ESTIMATES

(5 Questions, Difficulty Level: EASY to MODERATE)

by Raison John J. Bassig

You have just designed a square function hall with a total area of 718.24 sq.m. Inside that area, there is a circular unpaved landscaping portion that measures 4.25m in radius. The rest of the function hall was specified to have wood-finish ceramic tile flooring. During your material selection, you have canvassed four (4) different brands that suits the function hall floor finish:

Brand A - 200mm x 1500mm tiles @ P125.50 per piece
Brand B - 150mm x 1200mm tiles @ P74.75 per piece
Brand C - 100mm x 900mm tiles @ P37.45 per piece
Brand D - 300mm x 300mm tiles @ P346.25 per box (with 9 pcs/box, ordered by the box)

Q#1: What is the total area of the surface to be provided with the wood-finish ceramic tile flooring?
a. 711.2 sqm
b. 691.5 sqm
c. 696.4 sqm
d. 661.5 sqm

The question can be solved by simply subtracting the floor area of the circular landscape from the total area of the entire square function hall. Recall that area of a circle is [π r²], where r is the radius. So,

Tiled Floor Area = [Square Function Hall Floor Area] - [Circular Landscape Floor Area]
Tiled Floor Area = [718.24sqm] - [π r²]
Tiled Floor Area = [718.24sqm] - [π x (4.25m)²]
Tiled Floor Area = [718.24sqm] - [~56.745...sqm]
Tiled Floor Area = ~661.5sqm

Therefore, the correct answer is d. 661.5 sqm.

Q#2: Which among the four brands, given their retail prices, would be the most economical in terms of material cost?
a. Brand A
b. Brand B
c. Brand C
d. Brand D

Given that all four tile brands have different sizes means that quantities of each material will be different to fill up the tiled floor area of the function hall. Moreover, the rate (prices and ordering units) are also different among the brands. So, we need to calculate the quantities of each brand of tiles and multiply it with the retail prices to determine which brand is the most economical.

Brand A: 200mm x 1500mm tile

Area of 1 Tile = 0.2m x 1.5m = 0.3sqm
Required Quantity for Brand A = [Tiled Floor Area] / [Area of 1 Tile]
Required Quantity for Brand A = [661.5sqm] / [0.3sqm/tile] = 2,205 tiles

Total Cost for Brand A = 2,205 tiles x P125.50/tile = P276,727.50

Brand B: 150mm x 1200mm tile

Area of 1 Tile = 0.15m x 1.2m = 0.18sqm
Required Quantity for Brand B = [Tiled Floor Area] / [Area of 1 Tile]
Required Quantity for Brand B = [661.5sqm] / [0.18sqm/tile] = 3,675 tiles

Total Cost for Brand B = 3,675 tiles x P74.75/tile = P274,706.25

Brand C: 100mm x 900mm tile

Area of 1 Tile = 0.1m x 0.9m = 0.09sqm
Required Quantity for Brand C = [Tiled Floor Area] / [Area of 1 Tile]
Required Quantity for Brand C = [661.5sqm] / [0.09sqm/tile] = 7,350 tiles

Total Cost for Brand C = 7,350 tiles x P37.45/tile = P275,257.50

Brand D: 300mm x 300mm tile (Note: ordered by the box only, with 9 pcs in 1 box)

Area of 1 Tile = 0.3m x 0.3m = 0.09sqm
Coverage Area of 1 Box = [Area of 1 Tile] x [Number of Tiles in 1 Box]
Coverage Area of 1 Box = [0.09sqm] x [9 pcs/box] = 0.81sqm/box
Required Quantity (Boxes) for Brand D = [Tiled Floor Area] / [Coverage Area of 1 Box]
Required Quantity (Boxes) for Brand D = [661.5sqm] / [0.81sqm/box] = 816.67 or 817 boxes

Total Cost for Brand D = 817 boxes x P346.25/box = P282,886.25

Therefore, the correct answer is b. Brand B (P274,706.25 is the most economical based on unit costs).

Q#3: If you select Brand D (which is ordered by the box), how many tiles will become extra pieces?
a. 2 pcs
b. 3 pcs
c. 5 pcs
d. 8 pcs

As we have computed in Q#2 above, the required number of boxes for Brand D tiles is [817 boxes]. Since Brand D tiles are only ordered by the box and there are 9 pcs of tiles in 1 box, then,

Total number of Brand D tiles ordered = 817 boxes x 9 tiles/box
Total number of Brand D tiles ordered = 7,353 tiles

We solve the question by simply determining the difference between total number of ordered tiles against the actual total number of Brand D (300mm x 300mm) tiles needed to be installed based on the tiled floor area of the function hall calculated in Q#1 as [661.5 sqm],

Required Quantity (Tiles) for Brand D = [Tiled Floor Area] / [Area of 1 Tile]
Required Quantity (Tiles) for Brand D = [661.5sqm] / [0.09sqm/tile]
Required Quantity (Tiles) for Brand D = 7,350 tiles

Extra Pieces of Tiles = [Total Number of Tiles Ordered] - [Required Quantity]
Extra Pieces of Tiles = [7,353 tiles] - [7,350 tiles]
Extra Pieces of Tiles = 3 tiles

Therefore, the correct answer is b. 3 pcs.

Q#4: Suppose the owner has approved Brand D as the floor finish along the outer edges of the function hall only, how many tiles will it take to fill up all-around such perimeter?
a. Approx. 356 pcs
b. Approx. 352 pcs
c. Approx. 360 pcs
d. Approx. 358 pcs

We first need to determine the lengths of the sides of the function hall. Note that the function hall is square, so, all sides will be the same. Since the area of the square function hall was already given as [718.24sqm], then,

Area of Square = (Side)²
Side = √(Area of Square)
Side = √(718.24sqm)
Side = 26.8m

Now that the dimensions of the sides are known, we then need to calculate how many pieces of Brand D (300mm x 300mm) tiles will it take to fill up 1 side of the function hall,

Required Tile Quantity Along 1 Side = [Side of Function Hall] / [Side of 1 Tile]
Required Tile Quantity Along 1 Side = [26.8m] / [0.3m/tile]
Required Tile Quantity Along 1 Side = 89.33 or Approx. 90 tiles

Since it will take ~90 pcs of Brand D tiles to fill up 1 side of the function hall (fully from end-to-end or wall-to-wall), and another ~90 pcs to fill up the opposite side of the function hall, the other remaining 2 sides will logically be "shorter" (from tile-to-tile only, as the four corners of the function hall has already been filled with tiles from the first 2 sides):

Side Length (Full End-to-End/Wall-to-Wall) = 26.8m
"Shorter Side" Length (Tile-to-Tile) = 26.8m - 0.3m (Tile already at corner) - 0.3m (Tile at other corner)
"Shorter Side" Length (Tile-to-Tile) = 26.2m

Computing for the quantity of tiles along the remaining sides,

Required Tile Quantity Along "Shorter" Side (Tile-to-Tile) = ["Shorter" Side of Function Hall] / [Side of 1 Tile]
Required Tile Quantity Along "Shorter" Side (Tile-to-Tile) = [26.2m] / [0.3m/tile]
Required Tile Quantity Along "Shorter" Side (Tile-to-Tile) = 87.33 or Approx. 88 tiles

So,

Grand Total Required Tile Quantity for All Sides = ~90 tiles + ~90 tiles + ~88 tiles + ~88 tiles
Grand Total Required Tile Quantity for All Sides = ~356 pcs
(Note: If you sum up using the decimal quantities, i.e., [89.33 + 89.33 + 87.33 + 87.33], considering that portions of cut tiles can still be re-used disregarding aligned grouting lines, then, the answer would be [353.32 or 354 tiles])

Therefore, the correct answer is a. Approx. 356 pcs.

Q#5: If the supplier of Brand A tiles gave you a discount of 3% for the first 1,000 tiles, 6% for the next 1,000 tiles, and the rest at 9%, how much will you save (if any) compared to ordering Brand B tiles?
a. P13,610.47
b. P11,589.22
c. P23,596.67
d. No savings, as Brand B tiles will still turn out to be cheaper than Brand A even at a discounted price.

As we have already computed in Q#2, the total quantity required for Brand A tiles is [2,205 pcs]. Calculating the discounted costs per batch of Brand A tiles, we have:

First 1,000 Tiles @ 3% Discount (i.e., offered at 97% of price) = 1,000 pcs x (P125.50 x 0.97) = P121,735.00
Next 1,000 Tiles @ 6% Discount (i.e., offered at 94% of price) = 1,000 pcs x (P125.50 x 0.94) = P117,970.00
Remaining 205 Tiles @ 9% Discount (i.e., offered at 91% of price) = 205 pcs x (P125.50 x 0.91) = P23,412.025

The total costs with discounts for Brand A tiles would be,

Total Cost of Brand A with Discounted Price = P121,735.00 + P117,970.00 + P23,412.025 = P263,117.025

As we have also already computed in Q#2, the total cost for Brand B tiles (without discounts) is [P274,706.25]. So, the savings for Brand A tiles at a discounted price compared to ordering Brand B tiles would then be,

Savings = [Total Cost of Brand B] - [Total Cost of Brand A at a Discounted Price]
Savings = [P274,706.25] - [P263,117.025]
Savings = [P11,589.225]

Therefore, the correct answer is b. P11,589.22.