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A shopkeeper sold a book at a loss of 14%. If the selling price had been increased by Rs. 100, there would have been a gain of 6%. What was the cost p
Question

A shopkeeper sold a book at a loss of 14%. If the selling price had been increased by Rs. 100, there would have been a gain of 6%. What was the cost price of the book?

A.

Rs. 650

B.

Rs. 500

C.

Rs. 970

D.

Rs. 450

Correct option is B

Given:
Initial loss percentage = 14%
If the selling price is increased by Rs. 100, the profit percentage becomes 6%.
Formula Used:

Loss % = CPSPCP×100\frac{ CP – SP}{CP} \times 100​​

Profit % = SPCPCP×100\frac{SP – CP} {CP} \times 100​​

Solution:
Let the cost price (CP) of the book be x.
Selling price at a loss of 14%:
SP (initial)=x×(114100)=0.86x\text{SP (initial)} = x \times (1 - \frac{14}{100}) = 0.86x​​
Selling price at a gain of 6%:
SP (increased)=x×(1+6100)=1.06x\text{SP (increased)} = x \times (1 + \frac{6}{100}) = 1.06x​​
Given that increasing the SP by Rs. 100 changes the loss to a gain:
0.86x + 100 = 1.06x
1.06x - 0.86x = 100
0.20x = 100
x = 1000.20\frac{100}{0.20} = 500
Thus, the cost price of the book is Rs. 500.

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