Question

Two bicycles were sold for Rs. $1000$ each, gaining $10\%$ on one and losing $10\%$ on the other.

The gain or loss $\%$ on the whole transaction is.

• A. $6$% Loss
• B. $8$% Loss
• C. $1$% Loss
• D. $2$% Loss

Answer 1

The correct option is C $1$% Loss

Selling price of two bicycles $=1000$ Rs. each

Let cost price of a bicycle on which gain is $10\%$ be $X$ Rs

and another bicycle on which lost is $20\%$ be $Y$ Rs.

Solving for bicycle on which gain is 10%,

We know that, $Sellingprice=Costprice+profit$

$\Rightarrow 1000=X+10\%ofX$

$\Rightarrow 1000=X+0.1X$

$\Rightarrow 1000=1.1X$

$\Rightarrow X=\frac{1000}{1.1}=\frac{10000}{11}$

Now, Solving for bicycle on which loss is 10%,

We know that, $Sellingprice=Costprice-loss$

$\Rightarrow 1000=Y-10\%ofY$

$\Rightarrow 1000=Y-0.1Y$

$\Rightarrow 1000=0.9Y$

$\Rightarrow Y=\frac{1000}{0.9}$

$\therefore Y=\frac{10000}{9}$

Now, $TotalCostprice=X+Y=\frac{10000}{11}+\frac{10000}{9}=\frac{200000}{99}=2020.20Rs$

and $TotalSellingprice=2\times 1000=2000Rs$

Since $Sellingprice<CostPrice$

So, In whole transaction, there is a $Lossof2020.20-2000=20.20Rs$

$\therefore LossPercentage=\frac{loss\times 100}{CostPrice}=\frac{20.20\times 100}{2000}=1.01\%=1\%\left(Approx\right)$