A rectangular portion of an airport runway was getting repaired for which an estimate was made on the basis of a rate Rs. R per square unit. But while doing the work, the length of the portion got increased by 10% and the breadth by 8%. Over and above this, there was an increase in the cost of the repair work to the extent of 15%. What was the overall percentage increase in the cost of repair over the estimate?
Answers
Given : Estimate of repair wok of portion of runways. 10 % increase in length , 8 % increase in breadth & 15 % increase in rate
To find : overall percentage increase in the cost of repair over the estimate
Solution:
Let say Length of portion of runway = L units
& Breadth of portion of runway = B units
Area = LB sq units
Cost Per sq unit = R
Total Cost = LBR
length of the portion got increased by 10%
=> New Length = L + (10/100)L = 1.1L
Breadth of the portion got increased by 8%
=> New Breadth = B + (8/100)L = 1.08B
New Area = 1.1L * 1.08B = 1.188 LB sq units
increase in the cost of the repair work to the extent of 15%
=> New Rate = R + (15/100)R = 1.15R
New Cost = 1.188LB * 1.15R = 1.3662LBR
increase in cost = 1.3662LBR - LBR = 0.3662LBR
overall % increase in Cost = (0.3662LBR / LBR) * 100
= 36.62 %
overall percentage increase in Cost = 36.62 %
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