Question

The marked price of a bicycle is ₹1,456. A shopkeeper allows a discount of 10% and gets a profit of 12%. Find the cost price of the bicycle.

• A. ₹1,370
• B. ₹1,070
• C. ₹1,170
• D. ₹1,270

Answer 1

Answer:

C. ₹1,170

The cost price of the bicycle is ₹1,170.

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Method 1: Finding Selling Price

1. Find the Selling Price (SP):

   • The shopkeeper gives a 10% discount on the Marked Price (MP) of ₹1,456.

   • $\text{Discount Amount} = 10\% \text{ of } 1,456 = 145.60$

   • $\text{SP} = \text{MP} - \text{Discount} = 1,456 - 145.60 = 1,310.40$

2. Find the Cost Price (CP):

   • The shopkeeper makes a 12% profit on the cost price.

   • $\text{SP} = \text{CP} \times \left(1 + \frac{\text{Profit}\%}{100}\right)$

   • $1,310.40 = \text{CP} \times 1.12$

   • $\text{CP} = \frac{1,310.40}{1.12} = 1,170$

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Method 2: Direct Ratio Method (Shortcut)

There is a direct relationship between Cost Price and Marked Price when both discount and profit percentages are known:
$\frac{\text{CP}}{\text{MP}} = \frac{100 - \text{Discount}\%}{100 + \text{Profit}\%}$

1. Substitute the values:
   $\frac{\text{CP}}{1,456} = \frac{100 - 10}{100 + 12}$
   $\frac{\text{CP}}{1,456} = \frac{90}{112}$

2. Solve for CP:
   $\text{CP} = \frac{90 \times 1,456}{112}$
   $\text{CP} = 90 \times 13 = 1,170$