Profit And Loss
Profit percent after weighing less
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 `=5\5/19%` or 5.26% Answer
Alternate method to calculate profit earns 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 `=5\5/19%` 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 `=1\1/9%` or 11.11% Answer
Alternate method to calculate profit earns 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 `=11\1/9%` 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 earns 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 `33\1/3%` or 33.33% Answer
Alternate method to calculate profit earns 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 `33\1/3%` 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 `11\1/9%` 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 `11\1/9%` 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 `=1/2xx100= 50%`
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 `=1/4xx100= 25%`
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 `=1.9/950xx1000 =$2`
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 `=0.5/1.5xx100= 33\1/3%`
Or, profit = 33.33%
Thus, overall profit of vendor `=33\1/3%` or 25% Answer
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