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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 - Fraudulent Trader

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6.6 Fraudulent Trader

Fraudulent trader questions involve purchasing or selling, less or more quantity than that has been promised. The approach for these questions is as follows.

1) Find the CP per stated unit and SP per stated unit. These stated values are the amounts that the trader promises to buy/sell at.
2) Find the CP per actual unit and SP per actual unit. These actual values provide the actual Profit %.

Example 15

Ramlal purchases rice at Rs. 2.472.472.47 per kg and marks up the price by 17%17 \%17% and sells it. He uses a defective weighing machine while selling the rice. It measures 900900900 gm of rice as 111 kg. What is Ramlal's profit percentage?

Solution

Note that we need to find the answer in percentage terms and 2.472.472.47 is a difficult number. We need not use it as we are required to find the profit %\%% and not the profit in Rupees.

∴ Let CP === Rs. 100100100 per 111 kg

SP per stated unit =100×1.17== 100 \times 1.17 ==100×1.17= Rs. 117\bm{117}117 per 1 kg

Due to the faulty weighing machine, trader actually sells 0.90.90.9 kg instead of 111 kg.

SP per actual unit === Rs. 117117117 per 0.90.90.9 kg

=Rs.1170.9kg=Rs.1301kg== \dfrac{\text{Rs.} 117}{0.9 \text{kg}} = \dfrac{\text{Rs.} 130}{1 \text{kg}} ==0.9kgRs.117​=1kgRs.130​= Rs. 130\bm{130}130 per 1\bm{1}1 kg

We need to use the actual CP and SP to find profit %\%%.

Profit %=SP−CPCP×100%=130−100100×100%=30%\% = \dfrac{\text{SP} - \text{CP}}{\text{CP}} \times 100 \% = \dfrac{130 - 100}{100} \times 100 \% = 30 \%%=CPSP−CP​×100%=100130−100​×100%=30%

Answer: 30%30 \%30%

Example 16

Jairaman claims to purchase and sell Jowar at the same price per kg. However, he uses a defective pan balance, wherein, 111 side weighs 200200200 grams more than the other. He uses a 111 kg weight for every purchase and sale, and he uses the balance to his advantage while buying and selling. What is his actual profit %\%%?

Solution

Let the CP and SP be Rs. 100100100 per kg. It is given that one side of the pan balance weighs 0.20.20.2 kg more than the other and he use the balance to his advantage.

While purchasing he would use the balance to his advantage by buying more, i.e., buy 1.21.21.2 kgs instead of the stated 111 kg.

Stated CP === Rs. 100100100 per 111 kg
Actual CP === Rs. 100100100 per 1.21.21.2 kg =Rs.1001.2kg= \dfrac{\text{Rs.}100}{1.2 \text{kg}}=1.2kgRs.100​

=Rs.2503= \bm{\text{Rs.} \dfrac{250}{3}}=Rs.3250​ per 1\bm{1}1 kg

While selling he would sell less, i.e., sell 0.80.80.8 kgs instead of the stated 111 kg.

Stated SP === Rs. 100100100 per 111 kg
Actual SP === Rs. 100100100 per 0.80.80.8 kg =Rs.1000.8kg= \dfrac{\text{Rs.} 100}{0.8 \text{kg}}=0.8kgRs.100​
=== Rs. 125\bm{125}125 per 1 kg

Profit %=125−25032503×100%=50%\% = \dfrac{125 - \dfrac{250}{3}}{\dfrac{250}{3}} \times 100 \% = 50 \%%=3250​125−3250​​×100%=50%

Answer: 50%50 \%50%

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