Profit, Loss & Discount · Topic 7 of 8

⚡ Selling-Price Shortcuts

2 exam question types, fully solved

Two question shapes where the profit% drops out of the numbers alone — you never need a single real rupee price.

Counts and scaling

CP of x articles = SP of y articles → profit% = . The base is the count actually SOLD (y), not the bigger count. If x > y it's a profit; if x < y a loss.

Selling price scaled: with CP fixed at 100 and old profit P,

• Double the SP → new profit% = 100 + 2P (not 2P).

• Half the SP → new profit% = (usually a loss).

Turn any loss into “cost recovered” first: a 17% loss means 83% of CP recovered.

📦CP of x = SP of yprofit% comes from the counts alone

x — CP articles

y — SP articles

“CP of 25 articles = SP of 20 articles”

CP side — 25 articles bought

SP side — 20 articles sold for that same money

profit% =(x − y)/y × 100=(25 − 20)/20 × 100=25%

▲x > y → PROFIT of 25%x > y

Why ÷ 20 (y), never ÷ 25 (x): let each article COST ₹1. Then CP of 25 = ₹25, so selling just 20 articles brings in ₹25 → SP per article = 25/20. Profit per article = 25/20 − 1 = 5/20 on a CP of ₹1 → profit% = (x − y)/y × 100. ⚠ Trap: the base is the count actually SOLD (y = 20) — dividing by x = 25 gives the wrong 20%.

CP of 20 = SP of 16 → profit% = = %.

Q1CP of 20 articles = SP of 16 articles. Profit% is:

Q2A man earns 50% profit. If he doubles the SP, new profit% is:

Q3SP of 12 articles = CP of 15 articles. Gain%:

📚

Real exam questions — Selling-Price Shortcuts

2 question types · 6 solved examples from real SSC papers

Article-count comparisons and SP-scaling tricks — the profit% drops out of the counts alone, no real price needed.

How to solve this type

Take CP of 1 article = ₹1. If "CP of x articles = SP of y articles", then ₹x is the selling price of y articles, so SP of 1 article =

\dfrac{x}{y}

and profit% =

\dfrac{x-y}{y}\times100

. If x > y it is a profit; if x < y it is a loss. To FIND a count when the profit% is given, use SP : CP = (100 + profit%) : 100, and remember the article counts run the OTHER way:

\dfrac{\text{bought}}{\text{sold}}=\dfrac{SP}{CP}

. The one golden rule that kills every trap: profit/loss% is always taken on the count actually SOLD, never on the larger comparison count.

CP of 50 articles = SP of x articles, and the profit is 25%. Find x.

A30B40C25D20

The SP of 34 articles equals the CP of 38 articles. Find the gain%.

10\dfrac{3}{17}\%

7\dfrac{6}{17}\%

9\dfrac{8}{17}\%

11\dfrac{13}{17}\%

Oranges are bought at 11 for ₹10 and sold at 10 for ₹11. Find the gain or loss%.

ALoss 21%BGain 21%CLoss 11%DGain 11%