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when a manufacturer allows 38% commission on the retail price of his product he earns a profit of 9%. what would be his profit percent if his commission is reduced by 22%?

Let the retail (marked) price of the product be RRR.

  • Commission allowed initially = 38%38%38% of RRR
  • So, manufacturer’s selling price to the agent = R−0.38R=0.62RR-0.38R=0.62RR−0.38R=0.62R
  • On this selling price, he earns a profit of 9%9%9%.
    So, Cost Price (CP) =0.62R1.09=\dfrac{0.62R}{1.09}=1.090.62R​.

Now the commission is reduced by 22% of its own value:

  • 22% of 38% = 0.22×38=8.360.22\times 38=8.360.22×38=8.36
  • New commission = 38%−8.36%=29.64%38%-8.36%=29.64%38%−8.36%=29.64% of RRR
  • New selling price to the agent = R−0.2964R=0.7036RR-0.2964R=0.7036RR−0.2964R=0.7036R.

New profit percent:

Profit=0.7036R−0.62R1.09\text{Profit}=0.7036R-\dfrac{0.62R}{1.09}Profit=0.7036R−1.090.62R​

Profit %=0.7036R−0.62R1.090.62R1.09×100\text{Profit %}=\dfrac{0.7036R-\dfrac{0.62R}{1.09}}{\dfrac{0.62R}{1.09}}\times 100Profit %=1.090.62R​0.7036R−1.090.62R​​×100

Compute the ratio:

Profit %=(0.7036×1.090.62−1)×100\text{Profit %}=\left(\dfrac{0.7036\times 1.09}{0.62}-1\right)\times 100Profit %=(0.620.7036×1.09​−1)×100

0.7036×1.09=0.766924,0.7669240.62≈1.236970.7036\times 1.09=0.766924,\quad \dfrac{0.766924}{0.62}\approx 1.236970.7036×1.09=0.766924,0.620.766924​≈1.23697

Profit %≈(1.23697−1)×100≈23.7%\text{Profit %}\approx (1.23697-1)\times 100\approx 23.7%Profit %≈(1.23697−1)×100≈23.7%

Answer: The manufacturer’s new profit percentage is approximately 23.7%.