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A shopkeeper claims to sell rice at cost price. He uses a false weight with the intention of selling rice at 20% profit. After selling rice to the customer, he realises that the customer has paid 15% less than what he should have paid. What is the actual profit percentage made by the shopkeeper?

a)2%gain

b)12%gain

c)4% gain

d)5% gain

Let the cost price of rice = $x$

Now shopkeeper sells at 20% profit by using false weight

$\therefore \text{selling price} = x + 0.2x = 1.2x$

Now customer has paid 15% less than what he should have paid

$\therefore \text{customer has paid} = 1.2x – (0.15)(1.2x) = 1.02x$

$\% \text{ of profit made by shopkeeper} = \frac{1.02x – x}{x}*100 = 0.02*100 = 2\%$

by

thank you..can this also be considered as right solution?

let cost of price =250;

and with 20% profit he should get 250+50=300 rupees from each customer

but customer paid only 85% which is 300*0.85=255 rupees customer paid

so if 50 rupees add on to cost makes 20% profit => then 5 rupees(as 255 only received) makes 5*20/50=2% profit..is this logic correct?
seems correct to me
Let cost price for the 1 Kg rice be 100 Rs.

for 20% profit he must have sold the rice for 120 Rs/kg
120Rs is selling price of 1Kg rice
then amount of rice he sells for 100Rs will be $1Kg *\frac{100}{120}$,
and cost price of $1*\frac{100}{120}$ Kg rice will be $1 *\frac{100}{120} * 100 Rs$ = 83.33
actual profit =$\frac{SP-CP}{CP}$*100

costomer pays 15% less i.e 85Rs instead of 100 RS
profit =$\frac{85-83.33}{83.33}$*100  =2%