Question

12. Sehar bought two dresses at 5000 each. She then
sold one of them at a loss of 10%. At what price
should she sell the second dress to gain 20% in all?​

Answer 1

Given :

Cost price of each dress : ₹5000

Loss percent of first dress : 10%

Overall gain percent : 20%

To find :

The gain percentage of second dress.

Solution :

First, we should find the selling price of both dresses.

Selling price of first dress :

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

$\sf \dashrightarrow \dfrac{(100 - 10)}{100} \times 5000$

$\sf \dashrightarrow \dfrac{90}{100} \times 5000$

$\sf \dashrightarrow \dfrac{9}{10} \times 5000$

$\sf \dashrightarrow \dfrac{9 \times 5000}{10} = \dfrac{45000}{10}$

$\sf \dashrightarrow \cancel \dfrac{45000}{10} = 4500$

Selling price of second dress :

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

$\sf \dashrightarrow \dfrac{(100 + x)}{100} \times 5000$

$\sf \dashrightarrow \dfrac{100 + x}{100} \times 5000$

$\sf \dashrightarrow \dfrac{100 + x}{1} \times 50$

$\sf \dashrightarrow 5000 + 50x$

Now, we should add the both cost prices and both selling prices.

Total cost price :

$\sf \dashrightarrow 5000 + 5000$

$\dashrightarrow$₹$\sf 10000$

Total selling price :

$\sf \dashrightarrow 4500 + 5000 + 50x$

$\sf \dashrightarrow 9500 + 50x$

Now, let's find the gain percentage of second dress.

Gain percentage of second dress :

$\sf \dashrightarrow Total \: gain \% = \dfrac{Gain}{CP} \times 100$

$\sf \dashrightarrow 20 = \dfrac{10000 - 9500 + 50x}{10000} \times 100$

$\sf \dashrightarrow 20 = \dfrac{10000 - 9500 + 50x}{10000} \times 100$

$\sf \dashrightarrow 20 = \dfrac{10000 - 9500 + 50x}{100}$

$\sf \dashrightarrow 20 \times 100 = 10000 - 9500 + 50x$

$\sf \dashrightarrow 10000 - 9500 + 50x = 2000$

$\sf \dashrightarrow 50x = 2000 - 10000 + 9500$

$\sf \dashrightarrow 50x = 1500$

$\sf \dashrightarrow x = \dfrac{1500}{50}$

$\sf \dashrightarrow x = 30\%$

Hence, the gain percentage of the second dress is 30%.