Question

Shanti sold two cameras Rs. 6555 each. On one she lost 5% , while on the other she gained 15%.Find the gain or loss per cent in the whole transaction.​

Answer 1

✬ Profit % = 4.04 % ✬

Step-by-step explanation:

Given:

• Selling price of each camera is Rs 6555.
• On first camera she lost 5%.
• On second camera she gained 15%.

To Find:

• What is the gain and loss percent in whole transaction ?

Solution: To find Cost price (C.P) when loss percent and selling price are given we use formula

★ C.P = S.P $\times$ 100/100 – Loss% ★

$\implies{\rm }$ C.P = (6555 $\times$ 100/100 – 5)

$\implies{\rm }$ C.P = (655500/95)

$\implies{\rm }$ C.P = Rs 6900

So, the Cost price of first camera is Rs 6900.

Now, Formula for Cost price when profit percent and selling price are given is

★ C.P = S.P $\times$ 100/100 + Profit% ★

$\implies{\rm }$ C.P = (6555 $\times$ 100/100 + 15)

$\implies{\rm }$ C.P = (655500/115)

$\implies{\rm }$ C.P = Rs 5700

So, the Cost price of second camera is Rs 5700.

∴ Total S.P of both cameras = 6555 + 6555

➙ Rs 13,110

∴ Total C.P of both cameras = 6900 + 5700

➙ Rs 12,600

Now compare both S.P & C.P

• S.P > C.P ( There is a profit )

➼ Profit = S.P – C.P

➼ Profit = 13,110 – 12,600

➼ Profit = Rs 510

As we know that

★ Profit% = ( Profit/C.P $\times$ 100 )

$\implies{\rm }$ Profit % = (510/1260 $\times$ 100)

$\implies{\rm }$ Profit % = 51000/1260

$\implies{\rm }$ Profit % = 4.04%

Hence, on whole transaction Shanti gained profit of 4.04%.

Answer 2

Solution :

$\bf{\large{\underline{\bf{Given\::}}}}$

Shanti sold two cameras Rs.6555 each. On one she lost 5% & other on she gained 15%.

$\bf{\large{\underline{\bf{Explanation\::}}}}$

$\underbrace{\sf{1_{st}\:Condition\::}}}$

• Shanti sell (S.P) one Camera is Rs.6555
• On one Camera loss = 5%
• Cost price = ?

$\bigstar$Using formula of the cost price, while become loss :

$\longrightarrow\sf{Cost\:price\:(C.P.)=\bigg (\dfrac{ 100\%}{100-Loss\%}\bigg)\times S.P.}\\\\\\\longrightarrow\sf{Cost\:price\:(C.P.)=\dfrac{100}{100-5}\times 6555} \\\\\\\longrightarrow\sf{Cost\:price\:(C.P.)=\dfrac{100}{\cancel{95}} \times \cancel{6555}}\\\\\\\longrightarrow\sf{Cost\:price\:(C.P.)=Rs.(100\times 69)}\\\\\\\longrightarrow\bf{Cost\:price\:(C.P.)=Rs.6900}$

$\underbrace{\sf{2_{nd}\:Condition\::}}}$

• Shanti sell (S.P) other camera is Rs.6555
• On other Camera gain = 15%
• Cost price = ?

$\bigstar$Using formula of the cost price, while become profit :

$\longrightarrow\sf{Cost\:price\:(C.P.)=\bigg (\dfrac{ 100\%}{100+gain\%}\bigg)\times S.P.}\\\\\\\longrightarrow\sf{Cost\:price\:(C.P.)=\dfrac{100}{100+15}\times 6555} \\\\\\\longrightarrow\sf{Cost\:price\:(C.P.)=\dfrac{100}{\cancel{115}} \times \cancel{6555}}\\\\\\\longrightarrow\sf{Cost\:price\:(C.P.)=Rs.(100\times 57)}\\\\\\\longrightarrow\bf{Cost\:price\:(C.P.)=Rs.5700}$

Now;

Total cost price of Camera = Rs.6900 + Rs.5700 = Rs.12600

Total selling price of Camera = Rs.6555 + Rs.6555 = Rs.13110

$\bf{S.P.>C.P}$

Profit = Selling price - Cost price

Profit = Rs.13110 - Rs.12600

Profit = Rs.510

So;

$\longrightarrow\sf{Profit\:\%=\bigg(\dfrac{Profit}{C.P.} \times 100\bigg)\%}}\\\\\\\longrightarrow\sf{Profit\:\%=\bigg(\dfrac{510}{126\cancel{00}} \times \cancel{100}\bigg)\%}\\\\\\\longrightarrow\sf{Profit\:\%=\bigg(\cancel{\dfrac{510}{126} }\bigg)\%}\\\\\\\longrightarrow\bf{Profit\:\%=4.047\%}$

Thus;

Shanti gain 4.047% in the whole transaction .