A retailer sold three products X, Y , and Z with selling prices in the ratio 3:5:7. He incurred a 12% loss on X, a 40% profit on Y , and broke even on Z. What was his overall profit or loss percentage?

The correct answer is Profit of 7.29%.

Step-by-Step Explanation:

Step 1: Express Selling Prices in terms of a variable

We are given the ratio of selling prices (SP) for products X, Y, and Z as 3:5:7.
Let the common ratio multiplier be k.

${\mathrm{SP}}_X=3k$

${\mathrm{SP}}_Y=5k$

${\mathrm{SP}}_Z=7k$

The total selling price (${\mathrm{SP}}_{\mathrm{total}}$) of all three products combined is:

${\mathrm{SP}}_{\mathrm{total}}=3k+5k+7k=15k$

Step 2: Calculate Cost Price (CP) for each product

For Product X: A 12% loss was incurred.
This means Selling Price is 88% of Cost Price ($100-12=88\%$).

${\mathrm{SP}}_X=0.88\times {\mathrm{CP}}_X$

${\mathrm{CP}}_X=\frac{3k}{0.88}=\frac{300k}{88}=\frac{75k}{22}$

For Product Y: A 40% profit was made.
This means Selling Price is 140% of Cost Price ($100+40=140\%$).

${\mathrm{SP}}_Y=1.40\times {\mathrm{CP}}_Y$

${\mathrm{CP}}_Y=\frac{5k}{1.4}=\frac{50k}{14}=\frac{25k}{7}$

For Product Z: The retailer broke even, which means Cost Price equals Selling Price.

${\mathrm{CP}}_Z={\mathrm{SP}}_Z=7k$

Step 3: Find Total Cost Price

Adding the cost prices of X, Y, and Z together:

${\mathrm{CP}}_{\mathrm{total}}=\frac{75k}{22}+\frac{25k}{7}+7k$

Taking the common denominator of 22 and 7, which is 154:

${\mathrm{CP}}_{\mathrm{total}}=\frac{(75\times 7)k+(25\times 22)k+(7\times 154)k}{154}$