GATE CSE 2024 | Set 2 | GA Question: 7

Question

​​​​​​A person sold two different items at the same price. He made $10 \%$ profit in one item, and $10 \%$ loss in the other item. In selling these two items, the person made a total of

• A. $1 \%$ profit
• B. $2 \%$ profit
• C. $1 \%$ loss
• D. $2 \%$ loss

Comments

Let's denote the cost price of each item as C.

For the item in which the person made a 10% profit:

Selling price = Cost price + 10% of cost price

Selling price = C + 0.1*C = 1.1C

For the item in which the person made a 10% loss:

Selling price = Cost price -10% of cost price

Selling price = C — O.1*C = 0.9C

Given that the total profit is \$100, we can set up the equation:

1.1C + 0.9C = C + 100

2C = C + 100

C = 100

So, the cost price of each item is \$100.

Now, let's calculate the total selling price:

$I.IC = 1.1 \times 100 = \$110$

For the item with 10% profit:

o.9C = 0.9 \times 100 = \$90

For the item with 10% loss:

Total selling price = \$110 + \$90 = $200

The total profit is the difference between the total selling price and the total cost price:

Total profit = \$200 - \$200 = \$0

So, the correct option is:

C. 2% loss

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Question  ache se poro... 2 bar na ho 3 times poro... den solve koro ...

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@vaishak2512

Cost Price can not be same as we are already given that selling price is same and one item produces profit while other item results in loss. 

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Try to take numbers in such questions

 

Answer 1

Let sp of one =100

1.profit at 10%

Cp+.1cp=100

Cp=90.9

2.Loss at 10%

Cp-.1cp=100

.9cp=100

Cp=111.1

Total cp=202.01

Total sp=200

Loss=-2.01

%=(2.01/202)*100=~1%

Answer 2

If the first profit/loss is $x\%$ and second profit/loss is $y\%$ then overall profit/loss $\%$ is calculated as:

$\text{Total profit/loss=x+y+$\frac{xy}{100}\%$}$

• we use $+$ sign if profit happens
• we use $-$ sign if loss happens

It is given that the first $10\%$ profit is followed by $10\%$ loss so overall ;

Total profit/loss=$10+(-10)+\frac{10*(-10)}{100}\%\implies\frac{-100}{100}\%=-1\%$

we know that the minus sign indicates loss so overall $1\%$ loss made by the person.

Option $(C)$ is correct.

Answer 3

This may help

Answer 4

1%loss

Comments

Let's denote the cost price of each item as C.

For the item in which the person made a 10% profit:

Selling price = Cost price + 10% of cost price

Selling price = C + 0.1*C = 1.1C

For the item in which the person made a 10% loss:

Selling price = Cost price -10% of cost price

Selling price = C — O.1*C = 0.9C

Given that the total profit is $100, we can set up the equation:

1.1C + 0.9C = C + 100

2C = C + 100

C = 100

So, the cost price of each item is $100.

Now, let's calculate the total selling price:

I.IC = 1.1 \times 100 = $110

For the item with 10% profit:

o.9C = 0.9 \times 100 = $90

For the item with 10% loss:

Total selling price = $110 + $90 = $200

The total profit is the difference between the total selling price and the total cost price:

Total profit = $200 - $200 = $0

So, the correct option is:

C. 2% loss