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By selling a cloth that is 3333m long, a draper loses an amount equal to the selling price of 33m of cloth. What is his loss %?

Solution

✅ Correct Option: 3

The draper sells 3333m of cloth and his loss equals the selling price of 33m of cloth.

Let Cost Price of 11m cloth =C= C and Selling Price of 11m cloth =S= S.


Cost Price of 3333m cloth =33C= 33C

Selling Price of 3333m cloth =33S= 33S

Loss =33C−33S= 33C - 33S


Loss equals selling price of 33m cloth:

33C−33S=3S33C - 33S = 3S

33C=33S+3S33C = 33S + 3S

33C=36S33C = 36S

C=36S33C = \dfrac{36S}{33}

C=12S11C = \dfrac{12S}{11}


Loss =33C−33S= 33C - 33S

=33×12S11−33S= 33 \times \dfrac{12S}{11} - 33S

=36S−33S= 36S - 33S

=3S= 3S


Cost Price =33C= 33C

=33×12S11= 33 \times \dfrac{12S}{11}

=36S= 36S


Loss %=LossCost Price×100\% = \dfrac{\text{Loss}}{\text{Cost Price}} \times 100

=3S36S×100= \dfrac{3S}{36S} \times 100

=336×100= \dfrac{3}{36} \times 100

=112×100= \dfrac{1}{12} \times 100

=813%= 8\dfrac{1}{3}\%

Therefore, the loss percentage is 813%8\dfrac{1}{3}\% or 8.33%8.33\%.

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