Question : A shopkeeper advertises for selling clothes at a 7% loss. However, by using a false scale of length 1 metre he gains 24%. What will be the actual length he uses instead of 1 metre?
Option 1: 75 cm
Option 2: 31 cm
Option 3: 76 cm
Option 4: 93 cm
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Correct Answer: 75 cm
Solution :
Let the length of scale be $x$ metres.
Let the cost price per meter cloth be Rs. 100
Now, the shopkeeper advertises to sell cloth at a 7% loss i.e. Rs. 93/metre
But actually, he sells $x$ meters for Rs. 93 and gains 24% profit
We know that cost price + profit = selling price
Now, the cost price of $x$ meter length cloth = 100$x$
So, the selling price of $x$ meter length cloth = 100$x$ + 24% of 100$x$
Thus, 100$x$ + 24% of 100$x$ = 93
⇒ 100$x$ + 24$x$ = 93
⇒ 124$x$ = 93
⇒ $x$ = 0.75 m = 75 cm
Hence, the correct answer is 75 cm.
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