Question

Luxmi sold two sarees for $Rs.2185$ each. On one she lost $5\%$, while on the other she gained $15\%$. Find her gain or loss per cent in the whole transaction.

Answer 1

Given:

Case1:

SP of one saree $=Rs.2185$
Gain percentage $=15\%$

let C.P of first saree $=x$

$\Rightarrow x\times (100+15)\%=2185$

$\Rightarrow x\times \left(115\right)\%=2185$

$\Rightarrow x\times \frac{115}{100}=2185$

$\Rightarrow x=2185\times \frac{100}{115}$

$\Rightarrow x=1900$

Therefore, C.P of one saree is $=Rs.1900$ ---(1)

Case 2:
SP of the other saree $=Rs.2185$
Loss percentage $=5\%$
Let CP of the other saree$=y$

$\Rightarrow y\times (100-5)\%=2185$

$\Rightarrow y\times \left(95\right)\%=2185$

$\Rightarrow y\times \frac{95}{100}=2185$

$\Rightarrow y=2185\times \frac{100}{95}$

$\Rightarrow y=2300$

Therefore, C.P of another saree is $=Rs.2300$ ---(2)

Now, the Total C.P $=Rs.2300+Rs.1900=Rs.4200$

Total S.P $=Rs.2185+Rs.2185=Rs.4370$

Here, S.P $>$C.P

$\Rightarrow$ Lakshmi will get gain.

Gain $=$ S.P $-$ C.P $=Rs.4370-Rs.4200=rS.170$

Gain percentage $=\frac{\text{Gain}}{\text{C.P}}\times 100$

$=\frac{170}{4200}\times 100$

$=4\frac{1}{21}$

Hence, Luxmi gains $4\frac{1}{21}\%$ in the whole transaction.