A shopkeeper marks the price of an article at ₹5,180. Find the cost price if after allowing a discount of 31% he still gains 5% on the cost price.​

Correct option is C

Given:

Marked Price (MP) = ₹5180

Discount = 31%

Gain = 5%

Formula Used:

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

Cost Price (CP) = SP ÷ $$(1 + \frac{\text{Gain}}{100})$$​​

Solution:

SP = $$5180 \times \left(1 - \frac{31}{100} \right)$$​​

= $$5180 \times 0.69$$​ = ₹3574.20

CP = $$\frac{SP}{1 + \frac{5}{100}}$$  = $$\frac{3574.20}{1.05}$$ = ₹3404 

Alternate Solution: 

​$$\frac{MP}{CP} = \frac{100 +profit}{100 - discount} \\ \ \\\ \frac{5180}{CP} = \frac{105}{69} \\ \ \\ CP = \frac{5180\times 69}{105} = 3404$$​​