Math: A shopkeeper fixed the price of a pen to make a profit of 10% .But he sold it allowing a discount of Rs 7.50 and lost 5%. At what price did he purchase the pen?
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The shopkeeper purchased the pen at Rs. 50

Step-by-step explanation:

Equations

Let's set

x = Original purchase price of the pen

The shopkeeper fixed the price of the pen to make a profit of 10%.

It means the retail price was going to be:

x + 10% x = x + 10x/100 = x + 0.1x = 1.1x

The retail price was fixed to 1.1x but the pen sold with a discount of Rs 7.50, thus the real retail price was

1.1x - 7.50

The shopkeeper lost 5% in the operation, thus:

1.1x - 7.50 = x - 5% x = x - 0.05x = 0.95x

The equation to solve is:

1.1x - 7.50 = 0.95x

Adding 7.50:

1.1x = 0.95x + 7.50

Subtracting 0.95x:

1.1x - 0.95x = 7.50

Operating:

0.15x = 7.50

Dividing by 0.15:

x = 7.50 / 0.15

x = 50

The shopkeeper purchased the pen at Rs. 50

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step-by-step explanation: