Honest Trader but Dishonest Weights

This is a typical type of profit and loss question in which a trader claims that he sells a commodity at cost price or sells at a low profit percentage, but uses a false weight, thereby gaining/losing money.

The basic formula applied in that case is:

Profit % = (100 x error)/(true weight – error)

Error = True weight – False weight

You will understand the concept better with the help of following examples:

Example 1:

A dishonest tradesman claims to sell his goods at cost price, but uses a weight of 800 gm for 1 kg. Find his gain percentage.

1.15%     2. 20%     3.  25%     4.22%

Solution:

Say, price of 1 gm = Rs. 1, so the 1kg = Rs. 1000.

For 800 gm amount, he charges amount for whole 1kg,

This means that, for selling good worth Rs 800, he charges Rs. 1000.

Therefore, CP = Rs. 800, and SP = Rs. 1000

⇒Profit = Rs. 200

Profit percentage = (200/800) x 1000 = 25%

Using the formula:

Percentage Profit earned = (100 x error)/(true weight – error)

= (100 x 200)/(1000 – 200) = 25%

Example 2:

A dealer sells his goods at cost price but unfortunately his machine is faulty and he incurs a loss of 20%. How much does the shopkeeper sell if the machine reads 1kg?

1. 1250 grams    2. 1300 grams  3.1225 grams    4.  1200 grams

Solution:

Let price of 1gm = Rs.1, so price of 1kg = Rs. 1000

As he’s selling 1kg amount (falsely) = Rs. 1000,

So SP = Rs. 1000.

Let CP = X ; SP = CP – Loss ;  0.80 X = 1000

Solving, we get, X = Rs.1250.

This means that he gives 1250 gm for 1 kg.

Example 3:

A shopkeeper sells his good at a profit of only 4%. But he gives 800 gms for 1 kg. What is his real profit percentage?

1. 25%     2. 30%     3. 40%     4.  35%

Solution:

Say, 1000 g costs Rs. 1000. As per the shopkeeper, he sells at a profit of 4%.

Thus, the selling price of 1000 gms. is, 1000 × 1.04 = Rs. 1040.

But, the quantity he has actually given is 800 gm, which cost him Rs. 800.

Therefore, he makes a profit of Rs. 1040 – 800 = Rs. 240.

Hence, profit percentage = 100 × 240/800 = 240/8 = 30%.

Example 4:

A shopkeeper sells his good at a loss of 2%. But he gives 700 gms for 1 kg. What is his real loss percentage?

1. 35%     2.  40%    3. 30%    4.  45%

Solution:

Say 1000 g costs Rs. 1000. As per the seller, he sells at a loss of 2%.

Thus, the selling price of 1000 gms is 1000 × 0.98 = Rs. 980.

But, the quantity given is 700 gm, which cost him Rs. 700.

Therefore, profit = 980 – 700 = Rs. 280.

⇒ Profit % = 100 × 280/700 = 280/7 = 40%