## Mar 17, 2017

### PROFIT AND LOSS

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Quantitative Aptitude Study Notes
Bank & SSC Exam

PROFIT AND LOSS
You know that quantitative aptitude section is most important in bank exams in PO and Clerk and for other competitive exams because if you want good score in bank exam then you have to score good in maths. In competitive exams the most important thing is time management, if you know how to manage your time then you can do well in Bank Exams. That’s where maths shortcut tricks and formula are comes into action. So continuously we are providing shortcut tricks on different maths topics.
The one of the most important topic in maths is PROFIT AND LOSS. You should know how to calculate profit and loss in very short time. For this here we are providing shortcut tricks and quicker method to calculate profit and loss in maths.

For profit and loss we use rule of fraction is dominant. We should understand this rule very well because it is going to be used in almost all the questions.
If our required value is greater than the supplied value, we should multiply the supplied value with a fraction which is more than one. And if our required value is less than the supplied value, we should multiply the supplied value with a fraction which is less than one.
If there is a gain of x%, the calculating figures would be 100 and (100 + x).
If there is a loss of y%, the calculating figures would be 100 and (100 - y).
If the required value is more than the supplied value, our multiplying fractions should be 100 + x / 100
Or
100 / 100 – y
(both are greater than 1).
If the required value is less than the supplied value, our multiplying fractions should be
Fractions should be 100 / 100 + x
Or
100 – y / 100
(Both are less than 1).
PROFIT = SELLING PRICE (SP) – COST PRICE (CP)
LOSS = COST PRICE (CP) – SELLING PRICE (SP)
To find the gain or loss per cent %
The profit or loss is generally reckoned as so much per cent on the cost.
GAIN OR LOSS PER CENT % = loss or gain × 100 / CP
CASE 1:
SIMPLE BASIC QUESTIONS FOR PROFIT AND LOSS:
Example 1: A woman buys a toy for 25 Rs and sells it for 30 Rs. Find her gain per cent?
Solution: Gain % = gain × 100 / CP
= 5 × 100 / 25
= 20%
Example 2: A girl buys a pen for 25 Rs and sells it for 20 Rs. Find her loss per cent?
Solution: Loss % = loss × 100 / CP
= 5 × 100 / 25
= 20%
Example 3: If a man purchases 11 oranges for 10 Rs and sells 10 oranges for 11 Rs. How much profit or loss does he make?
Solution:
Suppose that the person bought 11 × 10 = 110 oranges.
CP of 110 oranges = 10 × 110 / 11 = 100 Rs.
SP of 110 oranges = 11 × 100 / 10 = 121 Rs.

Profit = 121 Rs – 100 Rs = 21 Rs
And % profit = profit × 100 / CP
= 21 × 100 / 100
=21%
We can also use shortcut method or quicker method for this type of questions:
Quicker method: rewrite the statements as follows:
Purchase                    11 oranges for 10 Rs.
Sell                              10 oranges for 11 Rs.
Now, percentage profit and loss is given by:
11 * 11 – 10 * 10  × 100
10 * 10
= 21%
Since the sign is +ve, there is a gain of 21%.
The above form of structural adjustment should be remembered. The first line deals with purchase whereas the second line deals with sales. Once you get familiar with the form, you need to write only the figures and not the letters.
Example 4: A man purchases 8 pens for 9 Rs and sells 9 pens for rupees 8. How much profit or loss does he make?
Solution: we will solve this questions quicker trick:
Purchases                  8 pens for 9 Rs
Sells                            9 pens for 8 Rs
% profit or loss = 8 × 8 – 9 × 9       × 100
9 × 9
= -1700/81
= -20.98%
Since the sign is –ve, there is a loss of 20.98%.
CASE 2:
Example 5: A dishonest dealer professes to sell his goods at cost price, but he uses a weight of 960 gm for the kg weight. Find his gain per cent.
Solution: suppose goods cost the dealer Re 1 per kg. He sells for Re 1 what cost him Re 0.96.
Gain on Re 0.96 = Re 1 – Re 0.96 = Re 0.04
Gain on Rs 100 = 0.04 × 100 / 0.96
= Rs 25 / 6
Gain % = 25/6%
We can also solve this question by using direct formula, it will save your time in the exam.
Direct formula:
% Gain  =                  ERROR                       × 100
True value – Error
Or
% Gain =  true weight – false weight     × 100
False weight
= 40 × 100 / 1000 – 40
=25/6%
CASE 3:
In the profit and loss topic the next example on;
TO FIND THE SELLING PRICE:
Example 6: A man bought a cycle for Rs 250. For how much should he sell it so as to gain 10%?
Solution:
If CP is Rs 100, the SP is Rs 110.
If CP is Rs 1, the SP is Rs 110 / 100.
If CP is Rs 250, the SP is Rs 110×250 / 100
= Rs 275.
Another suggested method (by rule of fraction)
If he wanted to sell the bicycle at a gain of 10%, the selling price (required value) must be greater than the cost price (supplied value), so we should multiply Rs 250 with a more than one value fraction. Since there is a gain, our calculating figures should be 100 and (100+10) and the fraction should be 110/100.
Thus, selling price = 250 × 110/100
= Rs 275.
CASE 4:
TO FIND THE COST PRICE:
Example 7: By selling goods for Rs 352.88, I lost 12%. Find the cost price?
Solution: CP should be more than SP; so we multiply SP by
100 / 100 – 12 = 100 / 88
(a fraction which is more than one)
CP = 352.88 × 100 / 88 = Rs 401.