Question

By selling a purse for Rs.$250$, Ranjana loses one-sixth of what it cost her. Fine (i)the cost price of the purse (ii) her loss percentage.
[Hint.$C.P.-S.P.=\frac{1}{6}ofC.P.\Rightarrow (1-\frac{1}{6})ofC.P.=\frac{5}{6}ofC.P.=$Rs.$250$ ]

Answer 1

$1)$Let the cost price of the purse be Rs.$x$.Then,

Loss$=\frac{1}{6}$ of Rs.$x=\frac{x}{6}$

Cost Price $=$ Selling Price $+$ Loss

$x=250+\frac{x}{6}$

$\Rightarrow x-\frac{x}{6}=250$

$\Rightarrow \frac{6x-x}{6}=250$

$\Rightarrow \frac{5x}{6}=250$

$\therefore x=250\times \frac{6}{5}=300$

Hence, the cost price of the purse is Rs.$300$.

$2)$Loss $=$ Cost Price $-$ Selling Price

$=$Rs.$300-250=$Rs.$50$

Loss$\%=\frac{Loss}{Costprice}\times 100=\frac{50}{300}\times 100=\frac{50}{3}\%$

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