A person purchases 100 pens at a discount of 10%. The net amount of money spent by the person to purchase the pens is Rs 600. The selling expenses incurred by the person are 15% on the net cost price. What should be the selling price for 100 pens in order

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Q: 5 (IAS/2008)
A person purchases 100 pens at a discount of 10%. The net amount of money spent by the person to purchase the pens is Rs 600. The selling expenses incurred by the person are 15% on the net cost price. What should be the selling price for 100 pens in order to earn a profit of 25%?

question_subject: 

Maths

question_exam: 

IAS

stats: 

0,3,2,1,0,3,1

keywords: 

{'selling price': [0, 0, 1, 0], 'net cost price': [0, 0, 1, 0], 'net amount': [0, 0, 1, 0], 'profit': [0, 0, 0, 1], 'selling expenses': [0, 0, 1, 0], 'discount': [0, 0, 1, 1], 'pens': [0, 0, 1, 0], 'rs': [0, 0, 9, 3]}

To find the selling price for 100 pens in order to earn a profit of 25%, we need to calculate the cost price of 100 pens and then add the desired profit.

Let`s break down the problem step by step:

1. The person purchases 100 pens at a discount of 10%. This means the person pays 90% of the original price for each pen.

Cost price of 100 pens = 100 pens * 90% of the original price per pen

2. The net amount of money spent by the person to purchase the pens is Rs 600.

Cost price of 100 pens = Rs 600

We can calculate the original price per pen using the formula:

Original price per pen = Cost price of 100 pens / (100 pens * 90%)

Let`s calculate the original price per pen:

Original price per pen = Rs 600 / (100 * 0.90) = Rs 6

Now that we know the original price per pen, we can calculate the selling price to earn a profit of 25%.

Profit percentage = 25%

Selling price = Cost price + Profit

Profit = Profit percentage * Cost price

Profit = 25% * Rs 600 = Rs 150

Selling price = Cost price + Profit

Selling price = Rs 600 + Rs 150 = Rs 750

However, we need to take into account the selling expenses incurred by the person, which are 15% on the net cost price.

Selling expenses = 15% * Cost price

Selling expenses = 15% * Rs 600 = Rs 90

Adjusted Selling price = Selling price + Selling expenses

Adjusted Selling price = Rs 750 + Rs 90 = Rs 840

Therefore, the selling price for 100 pens in order to earn a profit of 25% is Rs 840.

Among the given options, none of them matches Rs 840. However, let`s calculate the percentage difference between the closest option and the calculated selling price to see which option is the closest.

Percentage difference = (Closest option - Calculated selling price) / Calculated selling price * 100

Option 1: Rs 802.50

Percentage difference = (802.50 - 840) / 840 * 100 ? -4.46%

Option 2: Rs 811.25

Percentage difference = (811.25 - 840) / 840 * 100 ? -3.35%

Option 3: Rs 862.50

Percentage difference = (862.50 - 840) / 840 * 100 ? 2.68%

Option 4: Rs 875

Percentage difference = (875 - 840) / 840 * 100 ? 4.17%

Among the given options, Option 3 (Rs 862.50) is the closest to the calculated selling price of Rs 840. Although it is not an exact match, it is the option with the smallest percentage difference.

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