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The cost of a washing machine is 25% less than the cost of a TV. If the cost of the washing machine increases by 82% and that of the TV decreases by 16%, then what is the change in the total cost of 8 washing machines and 9 TVs?
Increase by 23.2%
Increase by 20%
Decrease by 24%
Decrease by 21%
Increase by 23.2%
Use the weighted average method: Change = [(Quantity1 * %Change1) + (Quantity2 * %Change2)] / Total Quantity. Here, total units = 8+9=17. Change = [(8 * 82) + (9 * -16)] / 17 = (656 - 144) / 17 = 512 / 17 тЙИ 30.11%? Wait, relative to cost base: Total Cost = 8(0.75T) + 9(T) = 6T + 9T = 15T. Change = (8 * 0.75T * 1.82 + 9 * T * 0.84) - 15T. Calculation: (6T * 1.82 + 9T * 0.84) - 15T = (10.92T + 7.56T) - 15T = 18.48T - 15T = 3.48T. Percentage = (3.48 / 15) * 100 = 23.2%.
Cost of 1 Washing Machine (W) = 75% of Cost of 1 TV (T). W = 0.75T. W increases by 82%, T decreases by 16%. Quantity: 8W and 9T.
Percentage┬аChange=Old┬аTotalNew┬аTotalтИТOld┬аTotalтАЛ├Ч100
Use the weighted average method: Change = [(Quantity1 * %Change1) + (Quantity2 * %Change2)] / Total Quantity. Here, total units = 8+9=17. Change = [(8 * 82) + (9 * -16)] / 17 = (656 - 144) / 17 = 512 / 17 тЙИ 30.11%? Wait, relative to cost base: Total Cost = 8(0.75T) + 9(T) = 6T + 9T = 15T. Change = (8 * 0.75T * 1.82 + 9 * T * 0.84) - 15T. Calculation: (6T * 1.82 + 9T * 0.84) - 15T = (10.92T + 7.56T) - 15T = 18.48T - 15T = 3.48T. Percentage = (3.48 / 15) * 100 = 23.2%.
Students often assume the total number of items is the divisor, forgetting to weight the percentage changes by the relative cost of the washing machine vs TV.
Define Cost Base
Assume TV cost T=100. Washing Machine cost W=0.75├Ч100=75.
T=100,W=75
Calculate Initial Total Cost
Initial Cost = 8├ЧW+9├ЧT=8(75)+9(100)=600+900=1500.
Initial=1500
Calculate New Total Cost
New W = 75├Ч1.82=136.5. New T = 100├Ч0.84=84. New Total = 8(136.5)+9(84)=1092+756=1848.
New=1848
Calculate Percentage Change
Change = 1848тИТ1500=348. Percentage Change = (348/1500)├Ч100=23.2%.
1500348тАЛ├Ч100=23.2%
A is correct because the total cost increased from 1500 to 1848, which is a 23.2% increase.
This logic is identical to 'Mixture and Alligation' problems where you calculate the average change of a group based on weightage.
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