# Profit and Loss Problems II- Complex Profit and Loss Problems

### If you are preparing for SBI PO, IBPS, SSC CGL or any other competitive exam, then Profit and Loss problems will definitely be on your to do list. In this post we’ll discuss different kinds profit and loss problems that are problems asked in Bank and SSC Exams.

Profit and loss problems can be very complex in nature and sometimes leave you in utter confusion wondering which formula to use form the list of profit and loss formulas. In the previous blog post in the series on profit and loss problems we discussed profit and loss formulas and basic problems based on it, it’s time to take a step forward and move to profit and loss problems that are more complex in nature, before we do that you must quickly revise the basic concepts and formulas!
We have picked up two kinds of profit and loss problems, that are asked in SBI PO, IBPS PO and SSC CGL, to discuss in this blog post- Profit and Loss Problems where SP and CP vary with respect to different Profit% and Loss% and Profit and Loss Problems based on Profit and Loss Relationship.

### Profit and Loss Problems Set I: Cost Price/ Selling Price when different Loss% and Profit% are given

Profit and loss problems discussed in this part are not based on direct formulas but need to you to adapt then apply the profit and loss formulas to the situation and then use them.

Problem 1: A watch was sold at a loss of 9%. It was observed that if the selling price was Rs.420/- more, then the profit made would have been 5%. What is the actual selling price of the watch?

Solution 1:
The ideal approach for you to solve to profit and loss problems of this kind should be to find SP in terms of percentage and then cross multiply to find the actual SP. The formulas to be used-
Step 1
We know that CP is always 100% and since there is a loss being incurred here,
SP = 100% - 9%
SP = 91%      (i)

Step 2
Assuming the new SP to be SP’, when the old SP is increased by 5%, we get
SP’ = 100% + 5%
SP’ = 105%     (ii)

Step 3
From the data given in the question we know that-
SP’ = SP + 420      (iii)

Step 4
Substituting (i) and (ii) in (iii), we get
105% = 95% + 420
14% = 420

Step 4
We know that the actual SP of the watch is 91%, therefore we can find the value of 91% by cross multiplication-
SP = (91 x 420) / 14
SP = 2730

Therefore the actual Selling Price of the watch is Rs.2730/-

If you go through the above method you’ll realize that you don’t need to write the 1st two steps in an exam, and therefore save time when you solve such profit and loss problems.

Problem 2: Praveen sold an article for Rs.1170 at the profit of 30%. What should be the selling point if the desired profit is 40%?

Solution 2:
The data given above clearly indicates Praveen made a profit and from the list of profit and loss formulas, we know the formula to calculate CP when a profit is made is-
Step 1
Substituting values in the above formula we get-
CP = [100 / (100 + 30)] x 1170
CP = 900

Step 2
Now we need to find the new SP is profit is 40%, for that we just need to substitute values in the formula-
SP = [(100 + 40) / 100] x 900
SP = 1260

Therefore the new Selling Price will be Rs.1260/-

Alternate Solution for Problem 2:
Another way to solve such profit and loss problems is by using the concept of percentages.

Step 1
We know CP=100% and if there is a profit of 30%, then
SP=130%
From the data given in the question, we know the SP of the article when it is sold at a profit of 30% is 1170.
130% = 1170      (i)

Step 2
The new SP, SP’ with 40% profit will be 140%     (ii)

Step 3
By cross multiplication we can find SP’-
SP’ = (140 x 1170) / 130
SP’ = 1260

Therefore the new Selling Price is Rs.1260/-

By using this method, you can eliminate useless steps and save time!

### Profit and Loss Problems Set II: Cost Price based on Profit and Loss Relationship

Profit and loss problems of this kind are very popular in bank exams any are expected to be there in SSC CGL 2017 too. In these profit and loss problems where profit made by selling the article at one value is equal to the loss incurred by selling the article at another value and form this data you have to find the cost price.

Problem 1: The profit earned by selling a phone for Rs.18000/- is the same as the loss incurred if the watch is sold at Rs.16800/- What is the cost price of the phone?

Solution 1:
The profit earned in situation one is equal to the loss incurred in situation 2. However, you must remember that in both the case, the Cost Price will remain the same.
Step 1
Profit = Loss
SPP – CP = CP – SPL      (i)

Step 2
Equating values in equation (i)
18000 – CP = 16800 – CP
2CP = 34800
CP = 17400

Therefore the Cost Price of the phone is Rs.17400/-

Problem 2: The profit earned by selling a shirt for Rs.1200/- is the same as the loss incurred if the shirt is sold for Rs.600/- What is the cost price of the shirt?

Solution 2:
Just like the previous profit and loss problems, in this problem too profit earned in situation one is equal to the loss incurred in situation 2. We already know both the case, the Cost Price will remain the same.
Step 1
Here profit is twice the loss, therefore from that we can derive-
Profit = 2Loss
SPP – CP = 2(CP – SPL)     (i)

Step 2
Equating values in equation (i)
1200 – CP = 2 x (600 – CP)
3CP = 2400
CP = 800

Therefore the Cost Price of the shirt is Rs.800/-

### Practice Profit and Loss Problems

Question 1: A watch was sold at a loss of 9%. It was observed that if the selling price was  420 more, the profit made would have been 5%. What is the actual selling price of the watch?
1)  2700      2)  2730      3)  3270      4)  3000      5) None of these

Question 2: After selling a book, Rohan found that he had made a loss of 12%. He also found that had he sold it for  36 more, he would have made a profit of 6%. What was the initial loss?
1)  12      2)  18      3)  20      4) Data inadequate      5) None of these

Question 3: The profit earned by selling an article for  625, is the same as the loss incurred by selling the article for  435. What is the cost price of the article?
1)  530      2)  520      3)  540      4)  550      5) None of these

Question 4: The profit earned by selling an article for  536, is the same as the loss incurred after the article for  426. What is the cost price of the article?
1)  448      2)  470      3)  481      4) ` 500      5) None of these