Question

A man sold 2 articles at Rs. 6000 each. These were sold at 25% gain and 25% loss respectively. Find gain or loss percent in the whole transaction?

Answer 1

Answer:

Loss of 6.67% incurred in the whole transaction.

Step-by-step explanation:

Selling prices of both the articles = Rs. 6000

Gain in one transaction = 25% (article I)

Loss in in one transaction = 25% (article II)

Cost Price of article I,

• SP = Rs. 6000
• Gain% = 25%
• CP = ??

⇒ CP = 100/(100 + Gain%) × SP

⇒ CP = 100/(100 + 25) × 6000

⇒ CP = 100/125 × 6000

⇒ CP = 600000/125

⇒ CP = 4800

Cost Price of article II,

• SP = Rs. 6000
• Loss% = 25%
• CP = ??

⇒ CP = 100/(100 - Loss%) × SP

⇒ CP = 100/(100 - 25) × 6000

⇒ CP = 100/75 × 6000

⇒ CP = 600000/75

⇒ CP = 8000

Gain/loss % in the whole transaction,

Total Selling price = 6000 + 6000 = Rs. 12000

Total Cost price = 4800 + 8000 = Rs. 12800

Cost Price > Selling Price

∴ Loss is incurred.

⇒ Loss % = (CP - SP)/SP × 100

⇒ Loss % = (12800 - 12000)/12000 × 100          

⇒ Loss % = 8/12 × 10

⇒ Loss % =  80/12

⇒ Loss % =  6.67% (approx)

Therefore, loss of 6.67% incurred in the whole transaction.

Answer 2

Given:

SP of each articles = Rs. 6000

Gain = 25%

Loss = 25%

Formula Used:

SP = CP × {(100 + Profit %)/100}

SP = CP × {(100 - Loss %)/100}

Loss% = {(CP - SP)/CP} × 100

Where,

SP = Selling price

CP = Cost price

Calculation:

Let the cost price of the first and second cycles is CP_1 and CP_2 respectively

Total SP = 6000 × 2

= 12000

According to the question, we have

$6000 = CP_1 × {(100 + 25)/100} \\ \\ ⇒ CP_ 1 = (6000 × 4)/5 \\ \\ ⇒ CP_ 1 = 4800.$$and \\ \\ 6000 = CP_ 2 × {(100 - 25)/100} \\ \\ ⇒ CP_2 = (6000 × 4)/3\\ \\ ⇒ CP_2 = 8000 \\ \\ Total \: \: CP = CP_1 + CP_2 \\ \\ ⇒ 4800 + 8000 \\ \\ ⇒ 12800.$

Now, total CP is greater than total SP

Loss % = {(12800 - 12000)/12000} × 100

⇒ (8/12)×10

⇒ 6.67%

∴ The total loss percentage is 6.67%.