Question:
A cycle was sold at a gain of 10%. Had it been sold for ₹ 260 more, the gain would have been 14%. Find the cost price of the cycle.
Solution:
Let the CP be ₹x.
SP when gain is $10 \%=x+\frac{10}{100} x=₹ \frac{110}{100} x$
SP when gain is $14 \%=x+\frac{14}{100} x=₹ \frac{114}{100} x$
Difference in SP = SP when gain is 14% − SP when gain is 10% = ₹260
$\therefore \frac{114 x}{100}-\frac{110 x}{100}=260$
$\Rightarrow \frac{4 x}{100}=260$
$\Rightarrow x=6500$
Hence, the CP of the cycle is ₹6,500.
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