Two classic shapes: two items sold at the same price (one gain, one loss), and one item described by two different selling situations.
The two shortcuts
1. Same SP, +x% and −x% → always a LOSS of 100x2 %. They never cancel, because the item sold at a loss had the higher cost. For x = 10 the loss is 1%; for x = 20 it is 4%.
2. Two conditions on one article → back out CP. Write each SP in terms of CP and subtract.
• If profit at one price = loss at another, CP is the midpoint of the two prices.
• Loss to profit spans (a + b)% of CP (you cross zero, so ADD); loss to loss spans only (a − b)% (SUBTRACT).
⚖️Two Articles, Same SP+x% and −x% never cancel
SP each (₹)
gain % (item 1)
loss % (item 2)
CP = SP ÷ (1 ± p/100)
Item 1 (sold at +20%): CP₁ = 600 ÷ 1.2 = ₹500
Item 2 (sold at −20%): CP₂ = 600 ÷ 0.8 = ₹750
Total CP = ₹1250 vs Total SP = ₹1200
⚠️ Classic trap — same SP, ±20% → always a LOSS. Shortcut: loss = x²/100 = 20²/100 = 4%. The loss item had the higher CP, so they never cancel.
Overall: 4% loss ₹50 lost on CP of ₹1250
Same SP at +10% and −10% gives an overall (100x2 = 1%).
📝Practice Questions
Q1Two items sold at the same SP, one at +10% and one at −10%. Overall:
Q2Same SP, +20% and −20%. Overall result:
Q3Profit selling at ₹1,500 equals loss selling at ₹1,300. CP is:
📚
Real exam questions — Two-Article Problems
2 question types · 6 solved examples from real SSC papers
Same SP, +x% and −x%? Always a loss of x²/100 %. And two conditions on one article pin down its CP.
How to solve this type
There is a famous shortcut here, and it has a twist most students get wrong. When two articles are sold at the SAME selling price, one at +x% profit and the other at −x% loss, the +x and −x do NOT cancel — the result is ALWAYS a net LOSS of 100x2%. (They would cancel only if the two COST prices were equal; here the SELLING prices are equal, so the costlier article — the one sold at a loss — drags the total down.) So the moment you see "same SP, +x% and −x%", write Loss = 100x2% and skip all the cost-price algebra. To turn that into a rupee figure: the total SP equals (100−100x2)% of the total CP, so scale from there.
A man sold two cars for ₹60,000 each. On one he gained 20%, on the other he lost 20%. The overall result is:
ANo profit/lossBLoss 2%CGain 4%DLoss 4%
A microwave and a dishwasher are each sold for ₹27,000, one at 25% profit and the other at 25% loss. The overall result is:
A7.75% profitB5.50% lossC6.25% lossD8.25% profit
A man sold two cars for ₹60,000 each, gaining 20% on one and losing 20% on the other. His overall loss (in ₹) is:
