Tips and Tricks and Shortcuts for Profit and Loss

Type 1 Problem- Seller has two Articles for same price, but first article is sold at  x% profit and other at x% loss. Total Profit/Loss incurred by him is not 0%

Way to solve this question is –

Apply direct formula Loss = ( \frac{x}{10})²%

Proof with example -> Let us assume the articles were sold at Rs1200, and 20% profit in case 1 is made and 20% loss in case 2 is made.

SP in case 1(Profit) – 1200

Thus CP = ( \frac{100}{100 + Gain} )× SP = ( \frac{100}{120}) × 1200 = ( \frac{5}{6}) × 1200 = 1000

SP in case 2(Loss) – 1200

Thus CP = ( \frac{100}{100 – Loss}) × SP = ( \frac{100}{80}) × 1200  = ( \frac{5}{4}) × 1200 = 1500

Total SP = 1200 + 1200 = 2400

Total CP = 1000 + 1500 = 2500

Loss = ( \frac{CP – SP}{CP}) × 100 = ( \frac{100}{2500}) × 100 = \frac{100}{25}= 4%

Also from direct formula above = ( \frac{20}{10})²

In such cases always, loss is incurred.

Type 2 Problem- Where no CP or SP is given. But whole concept is about Percentages.

Way to Solve Type 2 Questions

Assume the CP to be 100 and then solve the whole problem.

Example. In a transaction, the profit percentage is 80% of the cost. If the cost further increases by 20% but the selling price remains the same, how much is the decrease in profit percentage?

Let us assume CP = Rs. 100.

Then Profit = Rs. 80 and selling price = Rs. 180.

The cost increases by 20% → New CP = Rs. 120, SP = Rs. 180.

Profit % = \frac{60}{120} * 100 = 50%.

Therefore, Profit decreases by 30%.

Type 3 Problem- There are two Articles and you have to calculate total loss or profit.

Way to solve type 3 Problem

Now these problems are generally easy. But the whole point of solving is not to even use a pen and solve in 20 seconds.

Example. A man bought some toys at the rate of 10 for Rs. 40 and sold them at 12 for Rs. 60. Find his gain or loss percent

Cost price of 10 toys = Rs. 40 → CP of 1 toy = Rs. 4.

Selling price of 12 toys = Rs. 60 → SP of 1 toy = Rs. \frac{160}{12} = 5

Therefore, Gain = 5 – 4 = 1.

Gain percent = \frac{1}{4}\times 100  = 25%

Now in your mind you must do value 4 and 5 and \frac{1}{4} = 25%.

Type 4 Problem- CP of y items is same as SP of x items and Profit or Loss of some percentage is made.

Way to solve type 4 Question

The cost price of 10 pens is the same as the selling price of n pens. If there is a loss of 40%, approximately what is the value of n?

Solution:

Let the price of each pen be Re. 1.

Then the cost price of n pens is Rs. n and

the selling price of n pens is Rs. 10.

Loss = n-10.

Loss of 40% → ( \frac{loss}{CP}) × 100 = 40

Therefore, \frac{n – 10}{n} × 100 = 40 → n = 17 (approx)

Type 5 Problem-

If the price of an item increases by r% , then the reduction in consumption so that expenditure remains the same is

or

If the price of a commodity decreases by r% then increase in consumption , so as not to decrease expenditure on this item is

Way to solve type 5 Questions

Just apply the following two formulas

Case 1

\left ( \frac{r}{100 + r} \right )\times 100%

Case 2

\left ( \frac{r}{100 – r} \right )\times 100%

Type 6 Problem(IMP)- A dishonest dealer claims to sell his goods at cost price ,but he uses a weight of lesser weight .Find his gain%.

Way to solve type 6 Problem

Apply the following formula directly

Gain % = \frac{True \: Weight – False\: Weight}{False \: Weight} × 100

Example. Shopkeeper bought a product for Rs1000 per kg and is selling that at the same price. However he uses, a weighing scale that gives scale of 1kg for every 800gms. What is his profit?

Answer will be( \frac{1000 – 800}{800})\times 100 = ( \frac{2}{8}) × 100 = 25% profit.

Type 7 Problem(IMP)-

These questions will not be there for exams like AMCAT and Cocubes etc but for eLitmus.

A shopkeeper sells an item at a profit of x % and uses a weight which is y % less .find his total profit

Use Formula: Gain% =

\left ( \frac{\%Profit +\%{ \text Less \: in \: weight}}{100 – \% { \text Less \: in \: weight}} \right )\times 100

When dealer sells goods at loss on cost price but uses less weight .

Profit% or Loss% = \left ( \frac{\%Less\: weight -\% Loss}{100 – \% Less\: in \: weight} \right )\times 100

A dishonest dealer sells goods at x % loss on cost price but uses a gms instead of b gms to measure as standard, his profit or loss percent :-

Use Formula: Profit% or Loss% = \left ( 100 – Loss\% \right )\left ( \frac{Original\: Weight}{Altered\: Weight} \right )- 100

Note :- profit or loss will be decided according to sign .if +ive it is profit ,if –ve it is loss .

Case-1: When dealer sells product at profit but alters weight

Profit% or loss% =  [100+gain%][ \frac{1000}{Altered \: Weight} ] – 100

Case-2: When dealer reduces weight in terms of percentage and earns profit 

Example: A shopkeeper sells an item at a profit of 20 % and uses a weight which is 20% less. Find his total profit.

Applying the first formula

( \frac{20+20}{100 – 20}) × 100 = 50%

Case-3: When dealer sells goods at loss on cost price but uses less weight.

Note :- profit or loss will be decided according to sign . If +ive it is profit ,if –ve it is loss.
Example: A dishonest dealer sells goods at 10% loss on cost price but uses 20%  less weight. Calculate profit or loss percent.

Solution:
Apply formula: Case 2 Formula

\left ( \frac{20-10}{100-20} \right )x 100

= \frac{25}{2}%

Here sign is positive so there is a profit of 12.5%

Case 4

Example: A dishonest dealer sells products at 10% loss on cost price but uses 2 gm instead of 4 gm . what is his profit or loss percent?

Solution:

Apply formula : 

[100-10] \frac{4}{2}-100 = 80%

Case 4

Note :- Profit or loss will be decided according to sign. If +ive it is profit ,if –ve it is loss .

Example: A shopkeeper uses 940 gm in place of one kg. He sells it at 4% profit. What will be the overall profit or loss?

Solve this on your own, answer is 10.6%