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Ratio & Proportion π Sample Questions & Solutions

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Ratio & Proportion A pitched roof is constructed with a pitch of 1 : 3 rise to span ratio. If the span of the roof is 4.8m, what is its rise 4.8 is = 3 parts so 4.8 ÷ 3 = 1.6 or 1 part 1.6 m = rise Or the rise is = 1/3 of the span = 1.6 m rise? 4.8m

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Ratio & Proportion Flat roofs have a fall that does not exceed 1 : 6 ratio of rise to run of falling surface ( 10° pitch approx.) e.g. A flat roof extends from the rear wall of a house over an extension that is 4.2m further out. Calculate the rise given a ratio of 1 : 9 4.2 ÷ 9 = 0.46m = 460 mm rise Answer

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Ratio & Proportion The recommended fall for 100mm PVC drainage pipe from a domestic dwelling is 1 : 40 On a run of 7.685m of 100mm waste pipe, by how much will the pipe fall from highest to lowest point assuming a 1 :40 gradient? 7.685 ÷ 40 = = 192mm Answer

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Ratio & Proportion If the cost of a carpentry project came to a total of €7,850, calculate the cost of each item listed when the ratio is as follows: Materials cost 2/5 Labour costs 3/10 Profit cost /10 VAT cost /5

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Ratio & Proportion Firstly, convert all fractions to the same denominator i.e. 2/5 to 4/10 & 1/5 to 2/10 Now we can divide our total by the denominator (10) so 7,850 ÷ 10 = 785 Material = 2/5 = 4/10 = 4 x 785 = €3,140 Labour = 3/10 = 3 x 785 = €2,355 Profit = 1/10 = 1 x 785 = €785 VAT = 1/5 = 2/10 = 2 x 785 = €1,570 3, , ,570 = €7,850

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