Question

Sonika sells two jewellery boxes for rupees 1400 each .on one she earn a profit of 10% and one another she suffers a loss of 10% find the overall profit or loss percent​

Answer 1

Given :

Selling price of a jewellery box : 1400

Profit percent of one box : 10%

Loss percent of other box : 10%

To find :

The overall profit or loss percentage.

Solution :

First, we should find the cost price of both the sets of jewellery boxes.

Cost price of first box :

$\sf \dashrightarrow \dfrac{100}{(100 + Profit\%)} \times SP$

$\sf \dashrightarrow \dfrac{100}{(100 + 10)} \times 1400$

$\sf \dashrightarrow \dfrac{100}{110} \times 1400$

$\sf \dashrightarrow \dfrac{10}{11} \times 1400$

$\sf \dashrightarrow \dfrac{10 \times 1400}{11} = \dfrac{14000}{11}$

$\sf \dashrightarrow \cancel \dfrac{14000}{11} = 1272.72$

Cost price of second box :

$\sf \dashrightarrow \dfrac{100}{(100 - Loss\%)} \times SP$

$\sf \dashrightarrow \dfrac{100}{(100 - 10)} \times 1400$

$\sf \dashrightarrow \dfrac{100}{90} \times 1400$

$\sf \dashrightarrow \dfrac{10}{9} \times 1400$

$\sf \dashrightarrow \dfrac{10 \times 1400}{9} = \dfrac{14000}{9}$

$\sf \dashrightarrow \cancel \dfrac{14000}{9} = 1555.55$

Now, we should find the total cost price and the selling price.

Total cost price :

$\sf \dashrightarrow 1272.72 + 1555.55$

$\sf \dashrightarrow Rs.2828.27$

Total selling price :

$\sf \dashrightarrow 1400 + 1400$

$\sf \dashrightarrow Rs.2800$

As we can see that the cost price is greater than selling price. So,

Loss rupees :

$\sf \dashrightarrow Cost \: price - Selling \: price$

$\sf \dashrightarrow 2828.27 - 2800$

$\sf \dashrightarrow Rs.28.27$

Now, we can find the loss percentage.

Loss percentage :

$\sf \dashrightarrow \dfrac{Loss}{Cost \: price} \times 100$

$\sf \dashrightarrow \dfrac{28.27}{2828.27} \times 100$

$\sf \dashrightarrow \dfrac{2827}{282827} \times 100$

$\sf \dashrightarrow \dfrac{2827 \times 100}{282827} = \dfrac{282700}{282827}$

$\sf \dashrightarrow \dfrac{282700}{282827} = 0.99\%$

Hence, the loss percentage on whole transaction is 0.99%.