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

Correct option is C

Given:

Marked price of the bicycle = ₹1,456

Discount allowed = 10%

Profit = 12%

Formula Used:​

SP = $$\text{MP} \times (1 - \frac{\text{Discount}}{100})$$​​

Profit = $$\frac{\text{Selling Price} - \text{Cost Price}}{\text{Cost Price}} \times 100$$​​

Solution:

Selling Price (SP) = $$1456 \times \left(1 - \frac{10}{100}\right)$$​​

​$$= 1456 \times 0.90 = ₹1,310.40$$​​

Now, 

​$$12 = \frac{1310.40 - \text{CP}}{\text{CP}} \times 100$$​​

​$$0.12 = \frac{1310.40 - \text{CP}}{\text{CP}}$$​​

​$$0.12 \times \text{CP} = 1310.40 - \text{CP}$$​​

​$$0.12 \times \text{CP} + \text{CP} = 1310.40$$​​

​$$1.12 \times \text{CP} = 1310.40$$​​

​$$\text{CP} = \frac{1310.40}{1.12} = ₹1,170$$

Alternate Solution: ​​

​$$\frac{MP}{CP} = \frac{100+profit\%}{100 - discount\%} \\ \ \\ \frac{1456}{CP}= \frac{112}{90} \\ \ \\ \implies CP = \frac{1456 \times 90}{112} = 1170$$