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The price of paint is increased by 12%. The cost of the labour is also increased by 15%. If the total cost of painting the room is directly proportional to the product of price of paint to the labour cost, then what is the percentage increase in the cost of painting the room?

The price of paint is increased by 12%. The cost of the labour is also increased by 15%. If the total cost of painting the room is directly proportional to the product of price of paint to the labour cost, then what is the percentage increase in the cost of painting the room? Correct Answer 28.8%

Let the original price of paint be 100x units

Let the original cost of labor be 100y units

According to the question,

Total cost of painting the room is directly proportional to the product of price of paint to the labour cost

Original cost of painting the room = 100x × 100y = 10000xy

Price of paint is increased by 12%

New price of paint = 100x + 12% of 100x = 112x

Cost of labour is increased by 15%

New cost of labour = 100y + 15% of 100y = 115y

New cost of painting the room = 112x × 115y = 12880xy

Increase in the cost of painting the room = 12880xy – 10000xy = 2880xy

Required percentage = {(Increase in cost)/(original cost)} × 100

Required percentage = (2880xy/10000xy) × 100 = 28.8%

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