Question

a shopkeeper bought two watch for rs.400. he sold them to gain 5% on one and lose 5% on the other. calculate his final gain or loss percent if the selling price of both watches is same.​

Answer 1

This is short cut for this type of questions, ie, gain or loss square/100=5^2/100=>0.25%loss

Always this type of questions will have loss

Answer 2

$L_n=0.25\%$ is the net loss percent.

Step-by-step explanation:

Given:

Cost of two watches, $CP_1+CP_2=400$

profit % on one watch, $P_1\%=5\%$

loss % on the other watch, $L\%=5\%$

Let the cost price of one watch be, $CP_1=x$

Then the cost price of the other watch, $CP_2=(400-x)$

amount of profit on watch 1,

$P=P\% \times CP_1$

$P=\frac{5}{100} \times x$

$P=\frac{x}{20}$

amount of loss on watch 2,

$L=L\% \times CP_2$

$L=\frac{5}{100} \times (400-x)$

$L=20-\frac{x}{20}$

Now, according to the question the selling prices are equal:

$SP_1=SP_2$

$CP_1+P=CP_2-L$

$x+\frac{x}{20} =(400-x)-(20-\frac{x}{20})$

$x=Rs. 190$

Now gain on one watch:

$P=\frac{190}{20} =Rs.\ 9.5$

Now loss on the other watch:

$L=20-9.5=Rs.\ 10.5$

Therefore we have net loss of:

$L_n=L-P$

$L_n=Re.\ 1$

Net loss percent:

$L_n\%=\frac{L_n}{CP_1+CP_2}\times 100$

$L_n=\frac{1}{400} \times 100=0.25\%$

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TOPIC: profit & loss

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