13 Jun 2017

Crack IBPS Exams 2017 - Topic wise Discussion on Quantitative Aptitude Day-1 (Profit and Loss) [Explanations Updated]

Crack IBPS Exams 2017 - Topic wise Discussion on Quantitative Aptitude Day-1 (Profit and Loss):
Dear Readers, We all knew a famous saying of the Legend Aristotle, “Well begun is half done” and we also knew that this statement is 100% true. To Crack the Bank Exams you need to know where to start and how to start. Now this is the absolute correct time to kick start the preparation for upcoming IBPS Exams 2017. To help you in this aspect and to be a part of your preparation here we, IBPS Guide Team providing Topic wise Discussion on Quantitative Aptitude, this session will be conducted regularly on daily basis. This will provide a complete overview on the topics along with exercise questions. Kindly Make use of it.

PROFIT AND LOSS
Points to Remember:
Cost Price (CP): The price at which an article is brought, including all costs such as transportation, taxes, etc.
Selling Price (SP): The price at which an article is sold.
Profit or Gain: If selling price is greater than cost price, the seller makes profit or gain. Gain = SP – CP.
Loss: If the SP is less than the CP then seller makes loss. Loss = CP – SP

Basic Formulae:
i) Gain = SP - CP
ii) Loss = CP – SP
iii) Gain% = {[(SP – CP) x 100]/CP}
iv) Loss% = {[(CP – SP) x 100]/CP}
v) A person sells an item at x% loss (+ sign) or x% profit (- sign). Had he sold that item for Rs. X more his profit would have been y%. Then
CP = [X/(y±x) × 100)
vi) If there is a loss of x% on selling an item at selling price (SP1) and also there is a profit of y% on selling price (SP2) then
SP2 = [SP1(100 + y)/(100 – x)]
vii) When a person sells two similar items, one at a gain of say x%, and at a loss of x%, then the seller always incurs a loss given by:
Loss% = (Common Loss and Gain%/10)2 = (x/10)2
viii) If a trader professes to sell his goods at CP, but uses false weights, then,
Gain% = [Error/(True value – error)]x100%
ix) If the Cost price of M articles is equal to the selling price of N articles then the profit percent is given by
P = [(M – N)/N] x 100
Marked Price or List Price: Price that is indicated or marked on the article is called marked price or MP.
Discount: It is reduction given on the Marked Price or List Price of an article.
Discount% = discount/MP x 100%;
Selling Price = (100 – d)/100 x MP
x) If an article is sold after allowing two successive discounts of d1% and d2% then selling price (S.P) is given by
S.P = [(100 – d1)/100] x [(100 – d2)/100] x MP
xi) Two successive discounts of d1 and d2 are equivalent to a single discount of
d = d1 + d2 – (d1 x d2/100)

Solved Example Questions on Profit and Loss:
Type 1:
1. Pankaj purchased an item for Rs.7500 and sold it at the gain of 24%. From that amount he purchased another item and sold it at the loss of 20%. What is his overall gain or loss?
Solution:
CP1 = Rs.7500; SP1 = 7500 x 124/100 = Rs.9300 = CP2
SP2 = 9300 x 80/100 = 7440. Here CP1 > SP2 (Hence, loss is incurred here)
Therefore Loss = 7500 – 7440 = Rs.60

Type 2:
2. Vijay purchased a Washing machine and a Television for Rs.15,400 and Rs.19,600 respectively. He sold washing machine for a profit of 15 percent and the television for a loss of 20 percent. What is his overall loss/profit?
Solution:
CP of WM = 15400, P = 15%; CP of Tel = 19600, L = 20%
SP of WM = 115/100 x 15400 = 17710; SP of Tel = 80/100 x 19600 = 15680
Total CP = 15400 + 19600 = 35000
Total SP = 17710 + 15680 = 33390
Since CP is greater than SP loss is occurred. Loss = 35000 – 33390 = 1610

Type 3:
3. If by selling an article for Rs 60, a person loses 1/7 of outlay (cost), what would he have gained or lost per cent by selling it for Rs.77?
Solution:
CP = SP/(1 – 1/7) = 60 x 7/6 = 70
Profit% = 77 – 70/70 x 100 = 10%

Type 4:
4. A producer of tea blends two varieties of tea from two tea gardens one costing Rs 18 per kg and another Rs 20 per kg in the ratio 5 : 3. If he sells the blended variety at Rs 21 per kg, then his gain percent is
Solution:
Suppose he bought 5 kg and 3 kg of tea
Cost Price = Rs. (5 x 18 + 3 x 20) = Rs. 150
Selling price = Rs. (8 x 21) = Rs. 168.
Profit = 168 - 150 = 18
So, Profit % = (18/150) * 100 = 12%

Type 5:
5. If books bought at prices ranging from Rs. 200 to Rs. 350 are sold at prices ranging from Rs. 300 to Rs. 425, what is the greatest possible profit that might be made in selling eight books?
Solution:
Least Cost Price = Rs. (200 * 8) = Rs. 1600.
Greatest Selling Price = Rs. (425 * 8) = Rs. 3400.
Required profit = Rs. (3400 - 1600) = Rs. 1800.

More Types on Profit and Loss Problems will be discussed in the next Session, Kindly follow us daily.

Exercise Questions:
1). Reha purchased a Scooty for Rs.54000/-. She sold it at a loss of 8 percent. With that money he again purchased another Scooty and sold it at a profit of 10 percent. What is his overall loss/profit?
a)   Loss of Rs.658/-
b)   Profit of Rs. 568/-
c)   Loss of Rs.638/-
d)   Profit of Rs.638/-
e)   None of these

2). Chandru purchased a Printer and a Washing machine or Rs.15400 and Rs.19600 respectively. He sold Printer for a profit of 15 percent and the Washing machine for a loss of 20 percent. What is his overall loss/profit?
a)   Loss of Rs.1620
b)   Profit of Rs.1620
c)   Loss of Rs.1610
d)   No gain no loss
e)   Cannot be determined

3). By selling an book for Rs. 144, a shopkeeper loses 1 / 7 of his outlay. By selling it for Rs. 168, his gain or loss percent is ?
a)   20% loss
b)   20% gain
c)   4 1/ 6 % gain
d)   4 1/6 % loss
e)   None of these

4). Arun owns a house worth Rs. 100000. He sells it to Mathi at a profit of 10% based on the worth of the house Mathi sell the house back to Arun at a loss of 10%. In this transaction Arun gets ?
a)   No profit no loss
b)   Profit of Rs . 10000
c)   Profit of Rs . 11000
d)   Profit of Rs . 20000
e)   None of these

5). If articles bought at prices ranging from Rs. 150 to Rs. 300 are sold at prices ranging from Rs. 250 to Rs 350, what is the greatest possible profit that might be made in selling 15 articles ?
a)   Rs. 2500
b)   Rs. 3000
c)   Rs. 3500
d)   Rs. 4500
e)   None of Above

6). Neepa blends two varieties of fruits - one costing Rs. 180 per kg and another costing Rs. 200 per kg in the ratio 5 : 3. If she sells the blended variety at Rs. 210 per kg, then her gain is :
a)   10%
b)   12%
c)   11%
d)   13%
e)   None of these

7). A cashew nut seller mixes three varieties of nuts costing 50, 20 and 30 per kg in the ratio 2 : 4 : 3 in terms of weight and sells the mixture at 33 per kg. What percentage of profit does he make ?
a)   8%
b)   10%
c)   9%
d)   11%
e)   None of these

8). An apple is sold at a certain price. By selling it at 2/3 of that price one loses 10%. The gain percent at original price is ?
a)   20%
b)   33 1/3%
c)   35%
d)   40%
e)   None of these

9). A man sells a Pulsar Bike to his friend at 10% loss. If the friend sells it for Rs. 54000 and gains 20%, the original C.P. of the Bike was?
a)   Rs. 25000
b)   Rs. 37500
c)   Rs. 50000
d)   Rs. 60000
e)   None of these

10). A Seller purchased some notes from a publication worth Rs. 750. Because of some reasons, he had to sell two-fifth part of the book at a loss of 15%. On which gain he should sell his rest of the notes, so that he gets neither nor loss
a)   10%
b)   9%
c)   12%
d)   15%
e)   None of these

Answers with Explanation for Exercise Questions:
1st SP = 2nd CP = Rs.54000 – 8% of Rs.54000.
= Rs.54000 – Rs.4320 = Rs.49680.
2nd  SP = Rs.49680 + 10% of Rs.49680
= Rs.49680 + Rs.4968 = Rs.54648.
:. Overall profit = 54648 – 54000 = Rs.648

The total CP = Rs.15400 + Rs.19600 = Rs.35000
SP of Printer = 15400+ its 15% = 15400 + 2310 = Rs.17710.
SP of Washing machine = 19600 – its 20% = 19600-3920 = Rs.15680.
Total SP = 17710 + 15680 = Rs.33390
:. Overall loss = 35000 – 33390 = Rs.1610

Let C.P. = Rs. P
S.P. = (C.P.) - (Loss) = P - P/7 = Rs. 6P/7
∵ 6P / 7 = 144
∴ P = (144 x 7) / 6 = Rs. 168
Hence, no Loss and no gain.

C.P. of Mathi = 110% of Rs. 100000 = Rs. 110000
Loss of Mathi = 10%
S.P. of Mathi = 90% of Rs. 110000 = Rs. 99000
Thus, C.P. of Arun = Rs. 99000
So, Arun gets [(10% of Rs. 100000) + (100000 - 99000)] = Rs. 11000

The greatest profit is possible only if the cost price of the articles is minimum and selling prices are maximum.
Let lowest cost price of the 15 articles = 150*15 = Rs. 2,250
Maximum selling price of 15 articles = 350 *15 = Rs. 5,250
So, maximum profit = 5250 - 2250 = Rs. 3,000

Let 5 kg of cheaper be mixed with 3 kg of dearer.
Then, Total C.P. = Rs. (180 x 5 + 200 x 3) = Rs. 1500
Total S.P. = Rs. (210 x 8) = Rs. 1680
Gain % = (180/1500 x 100) % = 12%

Let 2x, 4x and 3x kg of three varieties be mixed.
Then, C.P. = Rs. [(2x × 50) + (4x × 20) + (3x × 30)] = Rs. 270x
S.P. = Rs. [(2x + 4x + 3x) × 33] = Rs. 297x
Gain % = (27x / 270x × 100) % = 10%

Let C.P. = Rs.100
S.P. at 10% loss = Rs. 90
∵ 2 / 3 of actual S.P. = Rs. 90
So, Actual S.P. = Rs. (90 x 3/2) = Rs. 135
∴ Gain = 35%

∵ S.P. = Rs. 54000
Gain earned = 20%
∴ C.P. = Rs. (100/120) x 54000 = Rs. 45000
Now, S.P. = Rs. 45000
And Loss = 10%
∴ Original C.P. = Rs. (100/90) x 45000 = Rs. 50000

Here, A = 2/5, R = 15%
According to the formula
Gain % = AR/(1 - A)%
= [(2/5) x 15]/[1 - (2/5)]%
= (6 x 5)/3%
= 10%

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