A cloth merchant says that due to slump in the market, he sells the cloth at 10% loss, but he uses a false metre scale and actually gain 20%. Find the actual length of the scale.

80 cm

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75 cm

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70 cm

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60 m

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Solution

The correct option is A 75 cm
We have
$\frac{100 + G}{100 + x} \frac{T r u e s c a l e}{F a l s e s c a l e}$ (See synopsis)

$\frac{100 + 20}{100 - 10} = \frac{100}{F a l s e s c a l e l e n g t h}$

$∴$ length of the scale used by the merchant $= 100 \times \frac{90}{120} = 75 c m$

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