A boy buys some pens for Rs.3 and an equal number for Rs.6. He sells them for Rs.7. What is his net loss%?

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20%

25%

30%

35%

answer is B.

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Detailed Solution

It is given that a boy buys some pens for Rs.3.
Let the number of pens be

x .

Therefore, the cost price for

x

pens are Rs.3.
Therefore, the cost price of 1 pen is,

C 1 = 3 x .

Also, the boy buys the same number of pens for Rs.6.
Therefore, the cost price for

x

pens are Rs.6.
Therefore, the cost price of 1 pen is,

C 2 = 6 x .

Now, the total number of pens

= x + x = 2 x .

It is given that the boy sells all the pens for Rs.7.
Therefore, the selling price of

2 x

pens are Rs.7.
Therefore, the selling price of 1 pen is,

S 1 = 7 2 x .

Case 1): Finding the gain %.
Here the cost price of 1 pen is

C 1 = 3 x .

The selling price of 1 pen is

S 1 = 7 2 x .

Since the selling price of 1 pen is greater than the cost price, therefore, there is a gain.
We know that the formula to find gain is given by,
Gain = Selling price - Cost price

⇒ Gain = 7 2 x − 3 x ⇒ Gain = 7 − 6 2 x = Rs . 1 2 x

∴ Gain % = Gain C .P . × 100 ⇒ Gain % = 1 2 x 3 x × 100 ⇒ Gain % = 100 2 × 3 = 503 % (1)

Case 2): Finding the loss %.
Here, the cost price of 1 pen is

C 2 = 6 x .

The selling price of 1 pen is

S 1 = 7 2 x .

Since the selling price of 1 pen is smaller than the cost price, therefore, there is a loss.
We know that the formula to find loss is given by,
Loss = Cost price - Selling price