Profit and Loss — BSSC Quantitative Aptitude

Explanation: Equating total CP and SP helps find the per-article CP to SP ratio.

• Solution: $15 \times CP = 10 \times SP \implies \frac{SP}{CP} = \frac{15}{10} = \frac{3}{2}$. Profit = $3 - 2 = 1$. Profit % = $(\frac{1}{2}) \times 100 = 50\%$.

• Exam Trick: Directly reverse the values: CP becomes 10, SP becomes 15. Profit is 5 on 10, which is exactly 50%.

Explanation: When the selling price of two articles is the same and the profit and loss percentages are equal, the overall transaction always results in a loss.

• Solution: Since SP is same and profit/loss is 20%, apply the formula for net loss: $\frac{a^2}{100}$%. Here $a = 20$. Loss = $\frac{20 \times 20}{100} = 4\%$.

• Exam Trick: Directly apply the $\frac{a^2}{100}$% loss formula. The absolute value (Rs. 5000) is redundant and should be ignored to save time.

Explanation: Successive discounts combine two sequential price drops into one effective drop.

• Solution: Let MP = 100. Price after 10% discount = 90. Price after a further 20% discount on 90 = $90 - 18 = 72$. Total discount = $100 - 72 = 28\%$.

• Exam Trick: Use the successive formula $a + b - \frac{ab}{100}$. Here, $10 + 20 - \frac{200}{100} = 30 - 2 = 28\%$.

Explanation: Profit is the combined successive effect of markup percentage and discount percentage.

• Solution: Let CP = 100. MP = 120. Discount = 10% of 120 = 12. SP = $120 - 12 = 108$. Profit = $108 - 100 = 8\%$.

• Exam Trick: Use the effective change formula: $a - b - \frac{ab}{100}$. Net change = $20 - 10 - \frac{200}{100} = 10 - 2 = 8\%$ profit.

Explanation: Discount is calculated based on the total number of items the customer walks away with.

• Solution: Total items = 4 (paid) + 1 (free) = 5. Free items = 1. Discount = $(\frac{1}{5}) \times 100 = 20\%$.

• Exam Trick: Apply ratio: $\frac{\text{Free}}{\text{Total}} \times 100$. So, $(\frac{1}{5}) \times 100 = 20\%$.

Explanation: Profit arises from giving less material than claimed. The cost price represents the actual weight given out by the shopkeeper.

• Solution: Goods given out = 900 g (his CP). Charged for = 1000 g (his SP). Ratio CP:SP = $900:1000 = 9:10$. Profit = 1. Profit % = $(\frac{1}{9}) \times 100 = 11.11\%$.

• Exam Trick: CP is what you give (900), SP is what you charge for (1000). Profit is 100 on 900. Directly $\frac{1}{9} = 11.11\%$.

Explanation: When profit is calculated on SP, the base value of the fraction represents SP instead of CP.

• Solution: 20% = $\frac{1}{5}$. If SP = 5, Profit = 1. CP = SP - Profit = $5 - 1 = 4$. Actual Profit % = $(\frac{1}{4}) \times 100 = 25\%$.

• Exam Trick: If profit on SP is $\frac{1}{x}$, the actual profit on CP is $\frac{1}{x-1}$. Here, $\frac{1}{5}$ converts to $\frac{1}{4} = 25\%$.

Explanation: To compare CP and SP fairly, the number of articles must be equated.

• Solution: LCM of 3 and 4 is 12. CP of 12 articles = $2 \times 4 = 8$. SP of 12 articles = $3 \times 3 = 9$. Profit = $9 - 8 = 1$. Profit % = $(\frac{1}{8}) \times 100 = 12.5\%$.

• Exam Trick: Cross multiply quantities and prices: CP = $2 \times 4 = 8$, SP = $3 \times 3 = 9$. Profit is 1 on 8, which is 12.5%.

Explanation: Since profit and loss are numerically equal, the Cost Price sits exactly in the middle of the two Selling Prices.

• Solution: Let CP be $x$. $x - 750 = 1250 - x \implies 2x = 2000 \implies x = 1000$.

• Exam Trick: When profit and loss are equal, simply add the two SPs and divide by 2: $\frac{750 + 1250}{2} = 1000$.

Explanation: Calculate SP directly from MP and compare it with the given CP percentage to find the profit.

• Solution: Let MP = 100. Then CP = 80. Discount = 12% of 100 = 12. SP = $100 - 12 = 88$. Profit = $88 - 80 = 8$. Profit % = $(\frac{8}{80}) \times 100 = 10\%$.

• Exam Trick: Assume MP is 100. SP is just $100 - \text{Discount}$. Gain is the difference between SP and CP on base CP. 8 on 80 is $\frac{1}{10}$ or 10%.