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

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6.3 SP of p units equals CP of q units.

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

Total CP == SP of pp units
Profit == SP of (q−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 \% =(q−p)p×100%= \dfrac{(q - p)}{p} \times 100 \%

Example 12

A trader purchased 8080 units of a product. After he sold 6060 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 \%

Alternatively

Let CP and SP of 11 unit of the product be cc and ss respectively.

SP of 6060 units == CP of 8080 units

⇒60s=80c⇒ 60s = 80c

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

⇒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),

Profit =33%= 33 \%

Answer: 33%33 \%

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

Total SP == SP of qq units
Profit == SP of pp units
CP == SP - Profit == SP of (q−p)(q - p) units

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

Example 13

When 1111 units of a product are sold, a trader's gain is the selling price of 33 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 \%

Alternatively

Let the selling price of a product be ss.

When 1111 units are sold,
SP =11s= 11s
Profit =3s= 3s
CP =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 \%

Answer: 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 pp units and get qq units free, we leave the store with a total of (p+q)(p + q) units. The discount here is the qq units that we get for free.

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

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

Example 14

Hotel Sarmani is running an offer, wherein for every 33 dosas purchased, 22 are given free. What is the maximum discount %\% that a customer can avail?

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

Solution

The minimum purchase (of 33 dosas) that provides the 22 free dosas is when the discount %\% is maximum.

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

Alternatively

Let the Marked Price of 11 dosa be mm.

As 55 dosas are sold for the value of 33 dosas,
Total Marked Price =5m= 5m
Total Discount =5m−3m=2m= 5m - 3m = 2m

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

Answer: 40%40 \%

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