6️⃣ By selling an article for ₹144, a person gains such a percentage that is numerically equal to the cost price. What is the cost price of the article?
Step-by-Step Explanation
Let the Cost Price (CP) be x.
Profit percentage = x%.
Selling Price (SP) = CP + (x/100)*CP.
144 = x + (x/100)*x.
14400 = 100x + x².
x² + 100x - 14400 = 0.
(x + 180)(x - 80) = 0.
x = -180 or x = 80.
Since cost price cannot be negative, CP = ₹80.
Answer: ₹80 ✅
7️⃣ A person sells two articles for ₹1710 each. On one, he gains 10%, and on the other, he loses 25%. What is his overall profit or loss?
Step-by-Step Explanation
SP of each article = ₹1710.
CP of first article = 1710 / 1.1 = ₹1554.55 (approx).
CP of second article = 1710 / 0.75 = ₹2280.
Total CP = 1554.55 + 2280 = ₹3834.55 (approx).
Total SP = 1710 * 2 = ₹3420.
Loss = 3834.55 - 3420 = ₹414.55 (approx).
Answer: ₹414.55 loss ✅
8️⃣ A trader sells an item at a profit of 20%. If he had bought it for 10% less and sold it for ₹12 less, he would have gained 30%. What is the cost price of the item?
Step-by-Step Explanation
Let the CP be x.
SP = 1.2x.
New CP = 0.9x.
New SP = 1.3 * 0.9x = 1.17x.
1.2x - 1.17x = 12.
0.03x = 12.
x = 12 / 0.03 = 400.
Answer: ₹400 ✅
9️⃣ A shopkeeper sells two types of rice. Type A costs ₹60 per kg, and type B costs ₹80 per kg. He mixes them in a ratio such that when he sells the mixture at ₹75 per kg, he gains 25%. What is the ratio in which he mixed the two types of rice?