Profit And Loss - Arithmetic

Question (1) A dishonest shopkeeper sells sugar at cost price. If he uses a weight of 950 gm instead of one kilogram, then find his profit percent.

Solution

Given, shopkeeper uses a weight of 950 gm instead of 1 kilogram

And sell the sugar at cost price, then gain % = ?

Less in weight = 1000 gm – 950 gm = 50 gm

Calculation of gain % by selling 50 gm less in one kg

Since, earning of shopkeeper on 950 gm = 50 gm

Therefore, earning of shopkeeper on 1 gm = 50 gm/950 gm

Therefore, earning of shopkeeper on 100 gm

Thus, profit of dishonest shopkeeper or 5.26% Answer

Alternate method to calculate profit earned by a dishonest dealer who weighs less

Given, shopkeeper uses a weight of 950 gm instead of 1 kilogram

And sell the sugar at cost price, then gain % = ?

Less in weight = 1000 gm – 950 gm = 50 gm

Here true value = 1000 gm.

Error in weight = 50 gm

We know that, in the case of weighing less

Thus, gain% for 50 gm error in 1000 gm

Thus, profit of dishonest shopkeeper or 5.26% Answer

Question (2) A dishonest shopkeeper sells rice at cost price. If he uses a weight of 900 gm instead of one kilogram, then find his profit percent.

Solution

Given, shopkeeper uses a weight of 900 gm instead of 1 kilogram

And sell the sugar at cost price, then gain % = ?

Less in weight = 1000 gm – 900 gm = 100 gm

Calculation of gain % by selling 100 gm less in one kg

Since, earning of shopkeeper on 900 gm = 100 gm

Therefore, earning of shopkeeper on 1 gm = 100 gm/900 gm = 1/9

Therefore, earning of shopkeeper on 100 gm

Thus, profit of dishonest shopkeeper or 11.11% Answer

Alternate method to calculate profit earned by a dishonest dealer who weighs less

Given, shopkeeper uses a weight of 900 gm instead of 1 kilogram

And sell the sugar at cost price, then gain % = ?

Less in weight = 1000 gm – 900 gm = 100 gm

Here true value = 1000 gm.

Error in weight = 100 gm

We know that, in the case of weighing less,

Thus, gain% for 100 gm error in 1000 gm

Thus, profit of dishonest shopkeeper or 11.11% Answer

Question (3) A dishonest shopkeeper sells his goods at cost price. If he uses a weight of 800 gm instead of one kilogram, then find his profit percent.

Solution

Given, shopkeeper uses a weight of 800 gm instead of 1 kilogram

And sell the sugar at cost price, then gain % = ?

Less in weight = 1000 gm – 800 gm = 200 gm

Calculation of gain % by selling 200 gm less in one kg

Since, earning of shopkeeper on 800 gm = 200 gm

Therefore, earning of shopkeeper on 1 gm = 200 gm/800 gm = 1/4 = 0.25

Therefore, earning of shopkeeper on 100 gm = 0.25 × 100 = 25%

Thus, profit of dishonest shopkeeper 25% Answer

Alternate method to calculate profit earned by a dishonest dealer who weighs less

Given, shopkeeper uses a weight of 800 gm instead of 1 kilogram

And sell the sugar at cost price, then gain % = ?

Less in weight = 1000 gm – 800 gm = 200 gm

Here true value = 1000 gm.

Error in weight = 200 gm

We know that, in the case of weighing less,

Thus, gain% for 200 gm error in 1000 gm

Thus, profit of dishonest shopkeeper 25% Answer

Question (4) A fruit seller sells orange at cost price. If he uses a weight of 750 gm instead of one kilogram, then find his profit percent.

Solution

Given, shopkeeper uses a weight of 750 gm instead of 1 kilogram

And sell the sugar at cost price, then gain % = ?

Less in weight = 1000 gm – 750 gm = 250 gm

Calculation of gain % by selling 250 gm less in one kg

Since, earning of shopkeeper on 750 gm = 250 gm

Therefore, earning of shopkeeper on 1 gm = 250 gm/750 gm = 1/3

Therefore, earning of shopkeeper on 100 gm

Thus, profit of dishonest shopkeeper or 33.33% Answer

Alternate method to calculate profit earned by a dishonest dealer who weighs less

Given, shopkeeper uses a weight of 750 gm instead of 1 kilogram

And sell the sugar at cost price, then gain % = ?

Less in weight = 1000 gm – 750 gm = 250 gm

Here true value = 1000 gm.

Error in weight = 250 gm

We know that, in the case of weighing less,

Thus, gain% for 250 gm error in 1000 gm

Thus, profit of dishonest shopkeeper or 33.33% Answer

Question (5) A shopkeeper offers selling potatoes at the cost price for the purchase of 5 kg. If he uses 4.5 kg weight instead of 5 kg, then what is the gain% of the shopkeeper?

Solution

Given, shopkeeper uses a weight of 4500 gm instead of 5000 kilogram

And sell the sugar at cost price, then gain % = ?

Less in weight = 5000 gm – 4500 gm = 500 gm

Calculation of gain % by selling 500 gm less in 5 kg

Since, earning of shopkeeper on 4500 gm = 500 gm

Therefore, earning of shopkeeper on 1 gm = 500 gm/4500 gm = 1/9

Therefore, earning of shopkeeper on 100 gm

Thus, profit of dishonest shopkeeper or 11.11% Answer

Alternate method to calculate profit earns by a dishonest dealer who weighs less

Given, shopkeeper uses a weight of 4500 gm instead of 5000 kilogram

And sell the sugar at cost price, then gain % = ?

Less in weight = 5000 gm – 4500 gm = 500 gm

Here true value = 5000 gm.

Error in weight = 500 gm

We know that, in the case of weighing less

Thus, gain% for 500 gm error in 5000 gm

Thus, profit of dishonest shopkeeper or 11.11% Answer

Question (6) A dishonest vendor purchase fruits at $5 per kg and sells it at $6 per kg. If he uses 800 gm weight instead of 1 kg, then what it his total profit?

Solution

Given, Cost price of fruit = $5 per kg

Sale price of fruit = $6 per kg

Correct weight should be used = 1kg = 1000 gm

Weight uses to sell 1 kg, i.e. 1000 gm = 800 gm

Thus, profit% = ?

Since the vendor uses 800 gm weight instead of 1000 gm, thus, selling price for 800 gm = $6

Thus, selling price for 1 gm = $6/800gm

Thus, selling price for 1000 gm

= $3 × 2.5 = $7.5

Thus, effective selling price for 1 kg = $7.5

Now, profit in selling of one kg of fruit = Sale price 1 kg of fruit – Cost price of 1 kg of fruit

= $7.5 – $.5 = $2.5

⇒ Profit per kg = $2.5

Now, in $5, the profit of vendor = $2.5

Therefore, in $1, the profit of vendor = $2.5/$5 = 1/2

Therefore, in $100, the profit of vendor

Thus, overall profit of vendor = 50% Answer

Alternate method to calculate profit earns by a dishonest dealer who weighs less

Here, cost price per kg = $5

And, effective selling price per kg after weighing less = $7.5

[As calculated above]

Thus, profit = Sale price – Cost price

= $7.5 – $5 = $2.5

Now, we know that

= 0.5 × 100 = 50%

Thus, profit = 50% Answer

Question (7) A dishonest vendor purchase fruits at $4 per kg and sells it at $4.5 per kg. If he uses 900 gm weight instead of 1 kg, then what it his total profit?

Solution

Given, Cost price of fruit = $4 per kg

Sale price of fruit = $4.5 per kg

Correct weight should be used = 1kg = 1000 gm

Weight uses to sell 1 kg, i.e. 1000 gm = 900 gm

Thus, profit% = ?

Since the vendor uses 900 gm weight instead of 1000 gm, thus, selling price for 900 gm = $4.5

Thus, selling price for 1 gm = $4.5/900gm

Thus, selling price for 1000 gm

Thus, effective selling price for 1 kg = $5

Now, profit in selling of one kg of fruit = Sale price 1 kg of fruit – Cost price of 1 kg of fruit

= $5 – $4 = $1

⇒ Profit per kg = $1

Now, in $4, the profit of vendor = $1

Therefore, in $1, the profit of vendor = $1/$4

Therefore, in $100, the profit of vendor

Thus, overall profit of vendor = 25% Answer

Alternate method to calculate profit earns by a dishonest dealer who weighs less

Here, cost price per kg = $4

And, effective selling price per kg after weighing less = $5

[As calculated above]

Thus, profit = Sale price – Cost price

= $5 – $4 = $1

Now, we know that

Thus, profit = 25% Answer

Question (8) A dishonest vendor purchase rice at $60 per bag and sells it at $76 per bag. One bag contains 40 kg of rice. If he uses 950 gm weight instead of 1 kg to sell the rice, then what it his total profit?

Solution

Given, 1 bag = 40 kg rice

Cost price of rice = $60 per bag

Thus, cost price of rice per kg = $60/40 = $1.50

And again, given the sale price per bag = $76

Thus, sale price per kg = $76/40 = $1.9

Thus, profit% = ?

But, as given again, the vendor uses 950 gm weight instead of 1kg

This means, sale price for 950 gm = $1.9

Therefore, sale price for 1 gm = $1.9/950

Therefore, sale price for 1000 gm

Thus, effective sale price per kg = $2

And cost price per kg = $1.5

Thus profit = sale price – cost price

= $2 – $1.5

⇒ Profit = $0.50

Now, in $1.5, the profit of vendor = $0.5

Therefore, in $1, the profit of vendor = $0.5/$1.5

Therefore, in $100, the profit of vendor

Or, profit = 33.33%

Thus, overall profit of vendor or 25% Answer