Calculating Cost Price from Loss and Gain Relationship

Let the Cost Price (CP) of the article be denoted by CP.

We are given two selling prices:

• SP1 = Rs. 2042 (at which a loss is incurred)
• SP2 = Rs. 2532 (at which a gain is attained)

Defining Loss and Gain

The loss incurred when selling at Rs. 2042 is calculated as:

Loss = CP - SP1 = CP - 2042

The gain attained when selling at Rs. 2532 is calculated as:

Gain = SP2 - CP = 2532 - CP

Formulating the Equation

The problem states that the loss is 75\% of the gain:

Loss = $75\%$ of Gain

Substituting the expressions for loss and gain:

CP - 2042 = $\frac{75}{100} \times (2532 - CP)$

Simplifying the fraction:

CP - 2042 = $\frac{3}{4} \times (2532 - CP)$

Solving for Cost Price

To solve for CP, we first multiply both sides by 4:

$4 \times (CP - 2042) = 3 \times (2532 - CP)$

Distribute the constants:

$4CP - 8168 = 7596 - 3CP$

Now, gather the CP terms on one side and the constants on the other:

$4CP + 3CP = 7596 + 8168$

$7CP = 15764$

Finally, divide by 7 to find the Cost Price:

CP = $\frac{15764}{7}$

CP = 2252

Conclusion

The cost price of the article is Rs. 2252.