Sujatha purchased two articles for a total of ₹1,080. By selling one at a profit of 25% and the other at a loss of 20%. She neither gains nor incurs a loss. What is the difference (in ₹) between the cost price of the two articles?
Show answer & explanation
Correct answer: A
Explanation
The correct answer is option 1 i.e. 120.
Let the cost price of first article = ₹x
Then, the cost price of second article = ₹(1080 − x)
Selling price of 1st article = x + 25% of x = x + 25/100 x = 125x/100 = 1.25x
Selling price of 2nd article = (1080 − x) − 20% of (1080 − x) = (1080 − x) × (1 − 20/100) = 0.8(1080 − x)
Total Selling Price = 1.25x + 0.8(1080 − x)
⇒ (1.25x − 0.80x) = 1080 − 864 ⇒ 0.45x = 216 ⇒ x = 216/0.45 = 480
First article: ₹480
Second article: ₹1080 − 480 = ₹600
Difference in cost prices = 600 − 480 = ₹120