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Discounts, Profit and Loss

Practice MCQs

This chapter deals with Discounts, Profit & Loss with many solved examples. Discounts: Discounts refer to a reduction in the original price of a product or service. Profit and Loss: Profit and loss, commonly abbreviated as P&L, is a financial statement that shows the net profit or loss of a business during a specific period.

Quantitative Aptitude Discounts, Profit and Loss Competitive Exams

Discounts, Profit and Loss is an important quantitative aptitude topic based on cost price, selling price, marked price, discount, profit percentage, and loss percentage.

What are Discounts, Profit and Loss?

The price at which an item is bought is called Cost Price. The price at which it is sold is called Selling Price. If selling price is more than cost price, there is profit. If selling price is less than cost price, there is loss.

Discount is the reduction given on the marked price or list price.

Quick idea: Profit and loss are calculated on Cost Price, while discount is calculated on Marked Price.
Term Meaning Short Form
Cost Price Price at which an item is bought CP
Selling Price Price at which an item is sold SP
Marked Price Price printed or listed before discount MP
Discount Reduction given on marked price D
Profit When selling price is greater than cost price SP > CP
Loss When selling price is less than cost price SP < CP

“In profit and loss, always identify CP, SP, and MP before applying formulas.”

Aptitude Tip
Key points
  • Profit or loss is calculated on cost price.
  • Discount is calculated on marked price.
  • If \(SP > CP\), there is profit.
  • If \(SP < CP\), there is loss.
  • Successive discounts are applied one after another.
  • Always check whether the answer should be amount or percentage.
CP SP MP discount

Important Formulas

Profit
\[ \text{Profit} = SP - CP \]

Used when \(SP > CP\).

Loss
\[ \text{Loss} = CP - SP \]

Used when \(SP < CP\).

Profit Percentage
\[ \text{Profit Percent} = \frac{\text{Profit}}{CP} \times 100 \]

Profit % is always calculated on CP.

Loss Percentage
\[ \text{Loss Percent} = \frac{\text{Loss}}{CP} \times 100 \]

Loss % is always calculated on CP.

Discount
\[ \text{Discount} = MP - SP \]

Difference between marked price and selling price.

Discount Percentage
\[ \text{Discount Percent} = \frac{\text{Discount}}{MP} \times 100 \]

Discount % is always calculated on MP.

SP with Profit

If profit is \(p\) percent:

\[ SP = CP \times \frac{100+p}{100} \]
SP with Loss

If loss is \(l\) percent:

\[ SP = CP \times \frac{100-l}{100} \]
Rule: Profit % and loss % are based on \(CP\), while discount % is based on \(MP\).

Common Types of Questions

Direct Profit

CP and SP are given. Find profit and profit percentage.

  • CP = ₹500
  • SP = ₹650
  • Profit = ₹150
  • Profit % = 30%
Direct Loss

CP and SP are given. Find loss and loss percentage.

  • CP = ₹800
  • SP = ₹720
  • Loss = ₹80
  • Loss % = 10%
Discount

MP and discount percentage are given. Find SP.

  • MP = ₹1000
  • Discount = 20%
  • Discount amount = ₹200
  • SP = ₹800
Successive Discount

More than one discount is applied one after another.

  • First discount 10%
  • Second discount 20%
  • Apply on reduced price
  • Not simply 30%
Exam approach: First identify whether the problem is based on \(CP\), \(SP\), \(MP\), profit, loss, discount, or successive discount.
Shortcut Method Bank
Profit Case

If profit is \(p\) percent:

\[ SP = CP \times \frac{100+p}{100} \]
Loss Case

If loss is \(l\) percent:

\[ SP = CP \times \frac{100-l}{100} \]
Discount Case

If discount is \(d\) percent:

\[ SP = MP \times \frac{100-d}{100} \]
Successive Discount

For discounts \(a\) percent and \(b\) percent:

\[ \text{Net Discount Percent} = a + b - \frac{ab}{100} \]

Tip: In successive discount, never add the two discount percentages directly.

Discounts profit and loss concept
Discounts, Profit and Loss questions are based on the relationship between cost price, selling price, marked price, discount, profit, and loss.

Step-by-Step Solving Method

Step Action Example
Step 1 Identify the given prices. CP = ₹500, SP = ₹650
Step 2 Check whether it is profit or loss. Since \(SP > CP\), it is profit.
Step 3 Find profit or loss amount. \(\text{Profit} = 650 - 500 = 150\)
Step 4 Find percentage if asked. \(\text{Profit Percent} = \frac{150}{500} \times 100 = 30\)
Step 5 Write final answer with correct unit. Profit = ₹150, Profit % = 30%
Important: In discount questions, start with \(MP\). In profit/loss questions, start with \(CP\).

Solved Examples

Question Method Answer
An item is bought for ₹500 and sold for ₹650. Find profit and profit percentage.
\[ \text{Profit} = SP - CP = 650 - 500 = 150 \]
\[ \text{Profit Percent} = \frac{150}{500} \times 100 = 30 \]
Profit = ₹150, Profit % = 30%
An item is bought for ₹800 and sold for ₹720. Find loss and loss percentage.
\[ \text{Loss} = CP - SP = 800 - 720 = 80 \]
\[ \text{Loss Percent} = \frac{80}{800} \times 100 = 10 \]
Loss = ₹80, Loss % = 10%
Marked price is ₹1000 and discount is 20%. Find selling price.
\[ \text{Discount} = \frac{20}{100} \times 1000 = 200 \]
\[ SP = 1000 - 200 = 800 \]
₹800
Cost price is ₹1200 and profit is 25%. Find selling price.
\[ SP = CP \times \frac{100+25}{100} \]
\[ SP = 1200 \times \frac{125}{100} = 1500 \]
₹1500
Cost price is ₹900 and loss is 15%. Find selling price.
\[ SP = CP \times \frac{100-15}{100} \]
\[ SP = 900 \times \frac{85}{100} = 765 \]
₹765
Marked price is ₹2000 and discount is 10% followed by 20%. Find final price.

First discount:

\[ 2000 \times \frac{90}{100} = 1800 \]

Second discount:

\[ 1800 \times \frac{80}{100} = 1440 \]
₹1440
An item is sold at 20% profit for ₹600. Find cost price.
\[ 600 = CP \times \frac{120}{100} \]
\[ CP = 600 \times \frac{100}{120} = 500 \]
₹500
An item is sold at 10% loss for ₹450. Find cost price.
\[ 450 = CP \times \frac{90}{100} \]
\[ CP = 450 \times \frac{100}{90} = 500 \]
₹500

Note: When SP is given along with profit or loss percentage, reverse the formula to find CP.

Practice

A) Multiple Choice Questions
  1. An item is bought for ₹400 and sold for ₹500. Find the profit.
    ₹50 ₹75 ₹100 ₹125
  2. An item is bought for ₹1000 and sold for ₹900. Find the loss percentage.
    5% 10% 15% 20%
  3. Marked price is ₹1500 and discount is 20%. Find selling price.
    ₹1000 ₹1100 ₹1200 ₹1300
  4. Cost price is ₹600 and profit is 25%. Find selling price.
    ₹700 ₹725 ₹750 ₹800
  5. Marked price is ₹1000. Two successive discounts of 10% and 20% are given. Find final price.
    ₹700 ₹720 ₹750 ₹800
B) Solve the Higher-Order Problems
  1. An article is sold at 20% profit for ₹720. Find the cost price. (Hint: \(SP = CP \times \frac{120}{100}\).)
  2. An article is sold at 15% loss for ₹850. Find the cost price. (Hint: \(SP = CP \times \frac{85}{100}\).)
  3. A shopkeeper marks an item at ₹2000 and gives a discount of 25%. Find the selling price. (Hint: Pay 75% of MP.)
  4. A trader buys an item for ₹1200 and sells it for ₹1500. Find profit percentage. (Hint: Profit percentage is based on CP.)
  5. An item has marked price ₹5000. Discounts of 20% and 10% are given successively. Find the final selling price. (Hint: Apply 20% first, then 10% on reduced price.)
C) Match the Term with the Correct Meaning
Term Correct Meaning / Formula
Profit \(SP - CP\)
Loss \(CP - SP\)
Profit Percentage \(\frac{\text{Profit}}{CP} \times 100\)
Loss Percentage \(\frac{\text{Loss}}{CP} \times 100\)
Discount \(MP - SP\)
Discount Percentage \(\frac{\text{Discount}}{MP} \times 100\)
Aptitude Reminder

Profit and loss questions depend on cost price and selling price, while discount questions depend on marked price and selling price. Always identify the base value before applying percentage formulas.

Task: Create five questions using direct profit, direct loss, discount, successive discount, and reverse CP calculation.

Show Suggested Answers
Multiple Choice
  1. ₹100
    \[ \text{Profit} = SP - CP = 500 - 400 = 100 \]
  2. 10%
    \[ \text{Loss} = 1000 - 900 = 100 \]
    \[ \text{Loss Percent} = \frac{100}{1000} \times 100 = 10 \]
  3. ₹1200
    \[ SP = MP \times \frac{100-20}{100} \]
    \[ SP = 1500 \times \frac{80}{100} = 1200 \]
  4. ₹750
    \[ SP = 600 \times \frac{125}{100} = 750 \]
  5. ₹720

    First discount:

    \[ 1000 \times \frac{90}{100} = 900 \]

    Second discount:

    \[ 900 \times \frac{80}{100} = 720 \]
Higher-Order Problems
  1. Sold at 20% profit for ₹720:
    \[ 720 = CP \times \frac{120}{100} \]
    \[ CP = 720 \times \frac{100}{120} = 600 \]
    Answer = ₹600.
  2. Sold at 15% loss for ₹850:
    \[ 850 = CP \times \frac{85}{100} \]
    \[ CP = 850 \times \frac{100}{85} = 1000 \]
    Answer = ₹1000.
  3. MP = ₹2000, discount = 25%:
    \[ SP = 2000 \times \frac{75}{100} = 1500 \]
    Answer = ₹1500.
  4. CP = ₹1200, SP = ₹1500:
    \[ \text{Profit} = 1500 - 1200 = 300 \]
    \[ \text{Profit Percent} = \frac{300}{1200} \times 100 = 25 \]
    Answer = 25%.
  5. MP = ₹5000. First discount 20%:
    \[ 5000 \times \frac{80}{100} = 4000 \]
    Second discount 10%:
    \[ 4000 \times \frac{90}{100} = 3600 \]
    Answer = ₹3600.
Concept Matching
  1. Profit → \(SP - CP\)
  2. Loss → \(CP - SP\)
  3. Profit Percentage → \(\frac{\text{Profit}}{CP} \times 100\)
  4. Loss Percentage → \(\frac{\text{Loss}}{CP} \times 100\)
  5. Discount → \(MP - SP\)
  6. Discount Percentage → \(\frac{\text{Discount}}{MP} \times 100\)
Clue Explanation

Profit and loss percentages are always calculated on cost price. Discount percentage is always calculated on marked price. This difference is the key to solving most exam questions correctly.

Exam tips
  • Always identify CP, SP, and MP first.
  • Profit/loss percentage is based on CP.
  • Discount percentage is based on MP.
  • Use reverse formula when SP and profit/loss percentage are given.
  • Apply successive discounts one after another.
  • Check whether the question asks for amount or percentage.
Practice MCQs