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**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.

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**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 1

^{st}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

SP

_{P}– CP = CP – SP_{L}(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

SP

_{P}– CP = 2(CP – SP_{L}) (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

Remember to
leave your answers in the comment section below!

And keep
practicing because only practice will make you perfect!

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