Quantity I: A shopkeeper marks an article 25% above its cost price. He gives a discount of 10% and earns a profit of ₹ 18.75. Find the cost price of the article.

Quantity II: A vendor buys 20 kg of rice at ₹50/kg and sells it at ₹60/kg. If he incurs a transportation cost of ₹100, find his net profit.

In the given question, two quantities are given, one as ‘Quantity I’ and another as ‘Quantity II’. You have to determine relationship between two quantities and choose the appropriate option. (Compare only numeric values)

Correct Answer: Quantity I > Quantity II

Let us calculate the numeric value for each quantity step-by-step to determine the correct relationship.

Step 1: Calculate Quantity I

Let the cost price (CP) of the article be ₹ x.

The shopkeeper marks the article 25% above its cost price.

$\text{Marked Price (MP)}=x+0.25x=1.25x$

He gives a discount of 10% on the marked price.

$\text{Discount}=10\%\text{of}1.25x=0.10\times 1.25x=0.125x$

$\text{Selling Price (SP)}=\text{MP}-\text{Discount}=1.25x-0.125x=1.125x$

Profit earned is given as ₹ 18.75.

$\text{Profit}=\text{SP}-\text{CP}$

$18.75=1.125x-x$

$18.75=0.125x$

$x=\frac{18.75}{0.125}=150$

So, Quantity I = 150.

Step 2: Calculate Quantity II

Total cost for buying 20 kg of rice at ₹ 50/kg:

$\text{Purchase Cost}=20\times 50=\text{₹}1000$

Transportation cost incurred = ₹ 100.

$\text{Total Cost Price (CP)}=1000+100=\text{₹}1100$

Total revenue from selling 20 kg of rice at ₹ 60/kg:

$\text{Total Selling Price (SP)}=20\times 60=\text{₹}1200$

$\text{Net Profit}=\text{SP}-\text{CP}=1200-1100=\text{₹}100$

So, Quantity II = 100.

Step 3: Compare Quantity I and Quantity II

Quantity I = 150

Quantity II = 100

Since 150 > 100, we have Quantity I > Quantity II.