A very Challenging Aptitude problem Profit and Loss
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Date: 2023-11-15
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Comments and reviews: 29
Jozsef6996
It depends of definition of profit rate. In microecomics the profit rate= total revenue/total cost-1, where the total revenue depends on selling price and quantity of sold items, and total cost depends on costs and quantity of resources and other cost e. g. labour, marketing, fixed costs etc. So when you say -Shopkeeper selling rice at profit 20%- that means the actual profit rate is 20% in microeconomics. What you have described in this excercise selling price of rice/kg=1. 2- buying cost of rice/kg but it is not the full coverage of profit.
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It depends of definition of profit rate. In microecomics the profit rate= total revenue/total cost-1, where the total revenue depends on selling price and quantity of sold items, and total cost depends on costs and quantity of resources and other cost e. g. labour, marketing, fixed costs etc. So when you say -Shopkeeper selling rice at profit 20%- that means the actual profit rate is 20% in microeconomics. What you have described in this excercise selling price of rice/kg=1. 2- buying cost of rice/kg but it is not the full coverage of profit.
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martin
I got it much easier. Watch this. Instead of wanting 1kg of rice and having the keeper add rice and and go through all that, I did this:
Customer requests 950g
Keeper adds rice until display says 950 (it's actually 1 kg in reality.
For simplicity, let's say 1kg is $1. 00. So basically the customer wants 95% of a kg according to the display. The keeper, unaware of the tampered machine, quotes him 1. 2x. 95 = $1. 14. Customer pays $1. 14. Keeper paid $1. 00 for the kg, reflecting to make $1. 20 on it. There's your 14%
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I got it much easier. Watch this. Instead of wanting 1kg of rice and having the keeper add rice and and go through all that, I did this:
Customer requests 950g
Keeper adds rice until display says 950 (it's actually 1 kg in reality.
For simplicity, let's say 1kg is $1. 00. So basically the customer wants 95% of a kg according to the display. The keeper, unaware of the tampered machine, quotes him 1. 2x. 95 = $1. 14. Customer pays $1. 14. Keeper paid $1. 00 for the kg, reflecting to make $1. 20 on it. There's your 14%
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TheGollywogofCoD
In this instance he thinks 1000 = 1000. But in reality, it-s 950 = 1000 because of tampering. Divide 1000 by 950 and you get 1. 05263. Multiply that by the now base of 1000 and you get 1053. 63. At this point, you divide 1200 (which is 1000 x 1. 2 (20% profit) by 1052. 63. That gives you 1. 14000171, or about 14% rounded. There-s your answer. Not sure if anyone finds this convoluted or difficult. It-s just how I mentally solved it.
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In this instance he thinks 1000 = 1000. But in reality, it-s 950 = 1000 because of tampering. Divide 1000 by 950 and you get 1. 05263. Multiply that by the now base of 1000 and you get 1053. 63. At this point, you divide 1200 (which is 1000 x 1. 2 (20% profit) by 1052. 63. That gives you 1. 14000171, or about 14% rounded. There-s your answer. Not sure if anyone finds this convoluted or difficult. It-s just how I mentally solved it.
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Dill
I figured it along the same lines as a lot of others, but looked at it on a cost basis just using the numbers presented:
Assume each gm of rice = 1 (in whichever currency)
Cost = 1
Sales Price = 1 - 120% = 1. 2
Total Sales = 950gm (weighed) - 1. 2 (sales price) = 1140
Total Cost = 1000gm (actual physical amount sold) - 1 = 1000
Profit: 1140 (sales) - 1000 (cost) = 140
Profit %: 140 (profit) / 1000 (cost) = 14%
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I figured it along the same lines as a lot of others, but looked at it on a cost basis just using the numbers presented:
Assume each gm of rice = 1 (in whichever currency)
Cost = 1
Sales Price = 1 - 120% = 1. 2
Total Sales = 950gm (weighed) - 1. 2 (sales price) = 1140
Total Cost = 1000gm (actual physical amount sold) - 1 = 1000
Profit: 1140 (sales) - 1000 (cost) = 140
Profit %: 140 (profit) / 1000 (cost) = 14%
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CaQ
Easiest way without all formulas:
1. Let -s say shopkeeper bought 1kg rice for $100 at $100perKg. Cost=$100
2. He is supposed to sell it for $120 at $120perKg (20% profit)
3. Due to faulty scale, as per his calculation, he will only be able to sell 950g of rice at $120 per kg.
4. Money he gets by selling 950g (at $120/kg) = 0. 95-120 = $114 = Selling Price.
5. Actual profit = (SellingPrice/Cost)-100 = 14%
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Easiest way without all formulas:
1. Let -s say shopkeeper bought 1kg rice for $100 at $100perKg. Cost=$100
2. He is supposed to sell it for $120 at $120perKg (20% profit)
3. Due to faulty scale, as per his calculation, he will only be able to sell 950g of rice at $120 per kg.
4. Money he gets by selling 950g (at $120/kg) = 0. 95-120 = $114 = Selling Price.
5. Actual profit = (SellingPrice/Cost)-100 = 14%
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Rishabh
But he has also kept th- profit margin of 20% in the addition 52. 5 g. So if we assume that the price of 1kg =1000 i. e 1 rupee per gram then the price for 1052. 5 g will be 1052. 5 rupees but now we-ll minus the price of 49. 875 of extra 52. 5 g grains ( cost price excluding 20% profit margin)
So now the cost for 1052. 5 grain will be. 1052. 5. And the profit will be 158 rupees and the profit percentage will be 15%
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But he has also kept th- profit margin of 20% in the addition 52. 5 g. So if we assume that the price of 1kg =1000 i. e 1 rupee per gram then the price for 1052. 5 g will be 1052. 5 rupees but now we-ll minus the price of 49. 875 of extra 52. 5 g grains ( cost price excluding 20% profit margin)
So now the cost for 1052. 5 grain will be. 1052. 5. And the profit will be 158 rupees and the profit percentage will be 15%
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Devon
Another way to look at it: say he sold the 950 g for 50 dollars then before that 20% 'profit' it was 41. 6666, but since its real weight was 1000 because the scale was tampered, then he should have gotten 41. 66 x 1000/950 = 43. 959. The relationship between 50 dollars and 43. 959 is 50 dollars is a 14 percent increase of 43. 959 SINCE 50 divided by 43. 959 = 1. 14 so he only received a 14% increase
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Another way to look at it: say he sold the 950 g for 50 dollars then before that 20% 'profit' it was 41. 6666, but since its real weight was 1000 because the scale was tampered, then he should have gotten 41. 66 x 1000/950 = 43. 959. The relationship between 50 dollars and 43. 959 is 50 dollars is a 14 percent increase of 43. 959 SINCE 50 divided by 43. 959 = 1. 14 so he only received a 14% increase
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Narendra
Consider The Purchase Price Of Rice - Rs 100
Selling Price Would Be - Rs 120
But, While Selling 1 Kg Rice He Is Paying For 1000x1000/950=1052. 6 Grams
Now, - Purchase Price Rs 100, The Seller Is Incurring Cost Of Rs 105. 26 For Every One Kg Rice Sold. And Hence His Profit Will Cut Down To Rs. 120-105. 26=14. 74 Rs For Every 105. 26 Rs. So His Profit Would Be 100x14. 74/105. 26=14. 0034%
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Consider The Purchase Price Of Rice - Rs 100
Selling Price Would Be - Rs 120
But, While Selling 1 Kg Rice He Is Paying For 1000x1000/950=1052. 6 Grams
Now, - Purchase Price Rs 100, The Seller Is Incurring Cost Of Rs 105. 26 For Every One Kg Rice Sold. And Hence His Profit Will Cut Down To Rs. 120-105. 26=14. 74 Rs For Every 105. 26 Rs. So His Profit Would Be 100x14. 74/105. 26=14. 0034%
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Rahul
It's way easy to solve the problem with my method.
He had 20%profit. means he got profit of 1rs on 5rs. Means he sell 5rs rice to 6rs.
Now he had a loss of 50 gm on 1000 gm. Means 5% loss. Means he sells 20 rs rice to 19 rs.
Now do successive calculation.
5 6
20 19
Means he sells 100rs rice to 114rs.
He got 14 rs profit on 100.
Therefore overall profit is 14%
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It's way easy to solve the problem with my method.
He had 20%profit. means he got profit of 1rs on 5rs. Means he sell 5rs rice to 6rs.
Now he had a loss of 50 gm on 1000 gm. Means 5% loss. Means he sells 20 rs rice to 19 rs.
Now do successive calculation.
5 6
20 19
Means he sells 100rs rice to 114rs.
He got 14 rs profit on 100.
Therefore overall profit is 14%
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Lame
Sorry sir, but i'm not agree with 14%
How?
Machine shows 1kg as 950 grams (1kg holds 1000 grams) so machine is tempered by 5%
When he make it 1kg on machine it is 1052. 5 grams, when he adds 50 grams to make it 1kg, actually he must add 52. 5 grams because machine is tempered by 5%.
So profit is slightly less than 14% not 14% exactly.
M lazy enough to calculate exact % -
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Sorry sir, but i'm not agree with 14%
How?
Machine shows 1kg as 950 grams (1kg holds 1000 grams) so machine is tempered by 5%
When he make it 1kg on machine it is 1052. 5 grams, when he adds 50 grams to make it 1kg, actually he must add 52. 5 grams because machine is tempered by 5%.
So profit is slightly less than 14% not 14% exactly.
M lazy enough to calculate exact % -
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Arif
When machine shows 950g actual weight is 1000 g.
But shopkeeper follows the machine reading.
Now, when machine shows 1000g actual weight is 1000 / 950 x 1000 = 1052. 63g
When actual weight is 1052. 63g selling price is 120 unit
So if actual weight is 1000g selling price will be
120 / 1053. 63 x 1000 unit = 114 unit.
Hence actual profit is 114 - 100 = 14%
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When machine shows 950g actual weight is 1000 g.
But shopkeeper follows the machine reading.
Now, when machine shows 1000g actual weight is 1000 / 950 x 1000 = 1052. 63g
When actual weight is 1052. 63g selling price is 120 unit
So if actual weight is 1000g selling price will be
120 / 1053. 63 x 1000 unit = 114 unit.
Hence actual profit is 114 - 100 = 14%
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Chrissy
Depends how you define profit, I always thought if you add 20% of purchase price onto goods, you have a 20% 'mark-up' but the actual profit percentage is measured compared to the Sale price. so a mark up of 25% gives you a profit of 20% meaning whatever money you receive from sales - 20% of it is profit. Not sure if that confused anyone else.
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Depends how you define profit, I always thought if you add 20% of purchase price onto goods, you have a 20% 'mark-up' but the actual profit percentage is measured compared to the Sale price. so a mark up of 25% gives you a profit of 20% meaning whatever money you receive from sales - 20% of it is profit. Not sure if that confused anyone else.
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imre
The problem is mistated if the seller was unaware he should be trust his weight and sell 1 kg for cogs of 0. 95 kg. That's all. You should not calculate the profit based on the biased weight additional weight the seller assuming the purchased 1 kg was correctly weighted. 50 gr is the absolute missing quantity from a cost pov.
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The problem is mistated if the seller was unaware he should be trust his weight and sell 1 kg for cogs of 0. 95 kg. That's all. You should not calculate the profit based on the biased weight additional weight the seller assuming the purchased 1 kg was correctly weighted. 50 gr is the absolute missing quantity from a cost pov.
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Siva
I consider 1 kg = 100 rs with profit he will get 120rs
For 10 kg he get 1200rs but he giving 10+10(0. 05)gms extra due to tampering
The total quantity was 10. 5kg for an amount of 1200 but amount of 0. 5kg is 60rs. So 200-60=140rs and he get 14% profit
I think my approach not appropriate but I got 14% as answer how?
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I consider 1 kg = 100 rs with profit he will get 120rs
For 10 kg he get 1200rs but he giving 10+10(0. 05)gms extra due to tampering
The total quantity was 10. 5kg for an amount of 1200 but amount of 0. 5kg is 60rs. So 200-60=140rs and he get 14% profit
I think my approach not appropriate but I got 14% as answer how?
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sayed-sarfaraz
E. g. 1Rs/gm then 1000rs for 1000gm
The customer given him 1000rs. But the customer should have given 52. 63Rs more bcz for making 1000gm shopkeeper added 52. 63gm more rice so, 200Rs(20% of 1000Rs) for 1000gm but he is not getting 200 instead he is getting 200-52. 63=147. 37Rs so 14. 73% is the correct answer.
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E. g. 1Rs/gm then 1000rs for 1000gm
The customer given him 1000rs. But the customer should have given 52. 63Rs more bcz for making 1000gm shopkeeper added 52. 63gm more rice so, 200Rs(20% of 1000Rs) for 1000gm but he is not getting 200 instead he is getting 200-52. 63=147. 37Rs so 14. 73% is the correct answer.
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logic_games
If you sell 1kg of rice for 120 monies, but bought it for 100 monies, your profit is 20%. Sell Price minus Buy Price equals Profit. If you give 1kg plus 1/19kg for 120 monies, then your buy price is 100 + 100/19 monies (approx. 105. 26. 120-(100+(100/19)=14, 7368. His profit is 14, 74%. Where is my mistake?
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If you sell 1kg of rice for 120 monies, but bought it for 100 monies, your profit is 20%. Sell Price minus Buy Price equals Profit. If you give 1kg plus 1/19kg for 120 monies, then your buy price is 100 + 100/19 monies (approx. 105. 26. 120-(100+(100/19)=14, 7368. His profit is 14, 74%. Where is my mistake?
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Peer
Seller: selling the rice of 1kg is 20% (1200gram. But unfortunately machine showing 950gram for 1kg.
He put extra rice 50 gm matching with 1kg. So the cost price is 1050gram, not 1kg.
Profit % = ( S. P - C. P) / C. P
= (1200-1050)/1050 = 14. 2%
This method is correct?
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Seller: selling the rice of 1kg is 20% (1200gram. But unfortunately machine showing 950gram for 1kg.
He put extra rice 50 gm matching with 1kg. So the cost price is 1050gram, not 1kg.
Profit % = ( S. P - C. P) / C. P
= (1200-1050)/1050 = 14. 2%
This method is correct?
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Jay
Not sure if this actually works or if I just got lucky, but I got the right answer and it-s much more simple.
Using 1. 2R as the selling price and figuring that he actually sells 95% of what he thinks he thinks he is, I just did 1. 2R -. 95 and got 1. 14R, which would give 14%
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Not sure if this actually works or if I just got lucky, but I got the right answer and it-s much more simple.
Using 1. 2R as the selling price and figuring that he actually sells 95% of what he thinks he thinks he is, I just did 1. 2R -. 95 and got 1. 14R, which would give 14%
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Aryan
let cost price of 1kg rice=100
so total profit of 1kg rice=20
cost of 50 gram rice=5 (by simple maths)
profit on 50 gram rice=1 (by simple maths)
so on subracting= 20-5-1=14
which will be actual profit. --
Please correct me if my approach is incorrect
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let cost price of 1kg rice=100
so total profit of 1kg rice=20
cost of 50 gram rice=5 (by simple maths)
profit on 50 gram rice=1 (by simple maths)
so on subracting= 20-5-1=14
which will be actual profit. --
Please correct me if my approach is incorrect
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DEBRAJ
It should be 15%
To sell 1000 kg, he has to add another 50gm to make it weigh 1000kg, i. e add 5% extra
Let cost price be=x
So selling price=1. 2x
Actual cost price = x+0. 05x
(5% extra)
Profit= 1. 2x - (x+0. 05x) = 0. 15x
i. e. 15%
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It should be 15%
To sell 1000 kg, he has to add another 50gm to make it weigh 1000kg, i. e add 5% extra
Let cost price be=x
So selling price=1. 2x
Actual cost price = x+0. 05x
(5% extra)
Profit= 1. 2x - (x+0. 05x) = 0. 15x
i. e. 15%
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Devon
14%. So, he actually sold 1, 000 gram (say at n per gram, where n is a currency ) and should therefore obtained (1000 x 1. 20) 1, 200 n in cash. Instead he obtained 1, 140 n (950 x 1. 2) but 1, 140 n is 14% greater than 1000 as 1000 x 1. 14 = 1, 140
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14%. So, he actually sold 1, 000 gram (say at n per gram, where n is a currency ) and should therefore obtained (1000 x 1. 20) 1, 200 n in cash. Instead he obtained 1, 140 n (950 x 1. 2) but 1, 140 n is 14% greater than 1000 as 1000 x 1. 14 = 1, 140
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education
Cost(100) + Profit(20) = SP(120)
Cost of goods sold-(1000/95)-100=105. 30
[Weighmachine shows 95% of physical stock we put. So, above formula]
So, Profit=SP(120)-Cost(105. 30)=14. 70
Pft % = 14. 70/105. 30=13. 96(apprx 14%)
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Cost(100) + Profit(20) = SP(120)
Cost of goods sold-(1000/95)-100=105. 30
[Weighmachine shows 95% of physical stock we put. So, above formula]
So, Profit=SP(120)-Cost(105. 30)=14. 70
Pft % = 14. 70/105. 30=13. 96(apprx 14%)
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Martin
The video mixes up profit and markup. The calculation price of 1. 2R is a 20% markup, which yields a profit of 16. 67%. The answer of 14% is the markup, not the profit percentage. (Profit is the percentage of sale price, not cost)
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The video mixes up profit and markup. The calculation price of 1. 2R is a 20% markup, which yields a profit of 16. 67%. The answer of 14% is the markup, not the profit percentage. (Profit is the percentage of sale price, not cost)
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Nataraajan
The actual profit in that case will be cost price+(selling price-cost price) of 50g rice+ (selling price-cost price) of 950g rice. So he'll pretty much earn additional profit when compared to what he calculated. I. e. 26. xx%
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The actual profit in that case will be cost price+(selling price-cost price) of 50g rice+ (selling price-cost price) of 950g rice. So he'll pretty much earn additional profit when compared to what he calculated. I. e. 26. xx%
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Tim
I said:
If someone asks for 950g the shopkeeper gives 1kg.
His profit should be 20% of 950g = revenue on 190g
But he gives an extra 50g so his profit is only the revenue on 140g over 1kg
140/(950 + 50) x 100 = 14%
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I said:
If someone asks for 950g the shopkeeper gives 1kg.
His profit should be 20% of 950g = revenue on 190g
But he gives an extra 50g so his profit is only the revenue on 140g over 1kg
140/(950 + 50) x 100 = 14%
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Omamba
You made that way more complicated than necessary. All you needed to do was find the ratio of rice given to weight displayed (1000g / 950g) and then divide the cost price by this ratio.
1. 2R / (1000g / 950g) = 1. 14R
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You made that way more complicated than necessary. All you needed to do was find the ratio of rice given to weight displayed (1000g / 950g) and then divide the cost price by this ratio.
1. 2R / (1000g / 950g) = 1. 14R
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Mathematics
Assume 1gm cost is Rs 1. So he sells 950 gm costing Rs950 with 20% profit at Rs1140. But it's 1kg, so actual cost is Rs 1000. So actual profit is Rs140 upon Rs 1000, so 14%.
Simple formula (950-1. 2 - 1000)/10
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Assume 1gm cost is Rs 1. So he sells 950 gm costing Rs950 with 20% profit at Rs1140. But it's 1kg, so actual cost is Rs 1000. So actual profit is Rs140 upon Rs 1000, so 14%.
Simple formula (950-1. 2 - 1000)/10
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Ravi
If he is unaware that the machine has been tampered, he will NOT add additional rice to the scale. Hence he is actually selling a lower quantity of rice for the same money, thereby his profit will be higher than 20%!
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If he is unaware that the machine has been tampered, he will NOT add additional rice to the scale. Hence he is actually selling a lower quantity of rice for the same money, thereby his profit will be higher than 20%!
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Louis
Assume 1000g rice costs $1000 and sells for $1200 (20% profit. The tampered scale causes the shopkeeper to sell 1000/950 = 1052. 6 g rice for $1200, so cost is $1052. 6. Actual profit is (1200-1052. 6)/1052. 6 = 14%
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Assume 1000g rice costs $1000 and sells for $1200 (20% profit. The tampered scale causes the shopkeeper to sell 1000/950 = 1052. 6 g rice for $1200, so cost is $1052. 6. Actual profit is (1200-1052. 6)/1052. 6 = 14%
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