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Arithmetic I

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Profit & Loss

Profit And Loss

MODULES

CP, SP & Profit
Marked Price
Successive Mark-up & Discount
P & L with Quantities
Fraudulent Trader
Other Types
FC, VC & Break-Even
Past Questions

CONCEPTS & CHEATSHEET

Concept Revision Video

SPEED CONCEPTS

Profit and Loss 1
-/10
Profit and Loss 2
-/10

PRACTICE

Profit & Loss : Level 1
Profit & Loss : Level 2
Profit & Loss : Level 3
ALL MODULES

CAT 2025 Lesson : Profit & Loss - P & L with Quantities

bookmarked

6.3 SP of p units equals CP of q units.

If SP of the first ppp units cover the CP of qqq units, then SP of the remaining (q−pq - pq−p) units is the profit.

Total CP === SP of ppp units
Profit === SP of (q−pq - pq−p) units

Profit % =SP of (q−p) unitsSP of p units×100%= \dfrac{\text{SP of} \space (q - p) \space \text{units}}{\text{SP of}\space p \space \text{units}} \times 100 \%=SP of p unitsSP of (q−p) units​×100% =(q−p)p×100%= \dfrac{(q - p)}{p} \times 100 \%=p(q−p)​×100%

Example 12

A trader purchased 808080 units of a product. After he sold 606060 of these units, he observed that his sales receipts equalled his total purchase cost. What is his profit percentage (rounded to the nearest integer)?

Solution

Directly applying the formula,

Profit %=80−6060×100%=33%\% = \dfrac{80 - 60}{60} \times 100 \% = 33 \%%=6080−60​×100%=33%

Alternatively

Let CP and SP of 111 unit of the product be ccc and sss respectively.

SP of 606060 units === CP of 808080 units

⇒60s=80c⇒ 60s = 80c ⇒60s=80c

⇒sc=43=1.33⇒ \dfrac{s}{c} = \dfrac{4}{3} = 1.33⇒cs​=34​=1.33

⇒s=c(1+0.33)⇒ s = c (1 + 0.33)⇒s=c(1+0.33)

As SP=CP×(1+p100)\text{SP} = \text{CP} \times \left(1 + \dfrac{p}{100} \right)SP=CP×(1+100p​),

Profit =33%= 33 \%=33%

Answer: 33%33 \%33%

6.4 Profit is SP of p units when q units are sold

Total SP === SP of qqq units
Profit === SP of ppp units
CP === SP - Profit === SP of (q−p)(q - p)(q−p) units

Profit %=p(q−p)×100%\% = \dfrac{p}{(q - p)} \times 100 \%%=(q−p)p​×100%

Example 13

When 111111 units of a product are sold, a trader's gain is the selling price of 333 units of a product. What is the trader's overall profit percentage?

Solution

Directly applying the formula,

Profit %=3(11−3)×100%=37.5%\% = \dfrac{3}{(11 - 3)} \times 100 \% = 37.5 \%%=(11−3)3​×100%=37.5%

Alternatively

Let the selling price of a product be sss.

When 111111 units are sold,
SP =11s= 11s=11s
Profit =3s= 3s=3s
CP =11s−3s=8s= 11s - 3s = 8s=11s−3s=8s

Profit %=ProfitCP×100%=3s8s×100%=37.5%\% = \dfrac{\text{Profit}}{\text{CP}} \times 100 \% = \dfrac{3s}{8s} \times 100 \% = 37.5 \%%=CPProfit​×100%=8s3s​×100%=37.5%

Answer: 37.5%37.5 \%37.5%


6.5 Buy p units and get q units free

In these kind of questions, we will be required to find the Discount %\%%.

When we buy ppp units and get qqq units free, we leave the store with a total of (p+q)(p + q)(p+q) units. The discount here is the qqq units that we get for free.

Total Marked Price === MP of (p+q)(p + q)(p+q) units
Total Discount === MP of qqq units

Discount %=DiscountMP×100%=q(p+q)×100%\% = \dfrac{\text{Discount}}{\text{MP}} \times 100 \% = \dfrac{q}{(p + q)} \times 100 \%%=MPDiscount​×100%=(p+q)q​×100%

Example 14

Hotel Sarmani is running an offer, wherein for every 333 dosas purchased, 222 are given free. What is the maximum discount %\%% that a customer can avail?

(1) 20%20 \%20%            (2) 33%33 \%33%            (3) 40%40 \%40%            (4) 67%67 \%67%           

Solution

The minimum purchase (of 333 dosas) that provides the 222 free dosas is when the discount %\%% is maximum.

Discount %=2(3+2)×100%=40%\% = \dfrac{2}{(3 + 2)} \times 100 \% = 40 \%%=(3+2)2​×100%=40%

Alternatively

Let the Marked Price of 111 dosa be mmm.

As 555 dosas are sold for the value of 333 dosas,
Total Marked Price =5m= 5m=5m
Total Discount =5m−3m=2m= 5m - 3m = 2m=5m−3m=2m

Discount %=2m5m×100%=40%\% = \dfrac{2m}{5m} \times 100 \% = 40 \%%=5m2m​×100%=40%

Answer: 40%40 \%40%

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