TOP 10 Important Shortcuts on Profit And Loss Problems for SBI Clerk / IBPS Exams 2017:
Dear Readers, Here we have given the TOP 10 Important Shortcuts on Profit and Loss Problems, candidates those who are preparing for the upcoming SBI Clerk/IBPS Exams 2017 can make use of it.
Basic Concept of Profit and Loss:
Cost Price (CP) –> Price at which an article is Purchase
Marked Price (MP) –> Price written on the article/MRP
Selling Price (SP) –> Price at which an article is sold
Profit –> SP> CP Profit = SP – CP
Loss –> CP> SP Loss = CP – SP
Profit% or Gain % –> Profit /CP ×100% = SP – CP / CP ×100%
Loss% –> Loss/CP ×100% = CP – SP / CP×100%
Rule of Fraction:
The gain of x% –> Calculate figure –> 100& 100 + x
The loss of x% –> Calculate figure –> 100& 100 – x
Example:
(A) If CP = 50, Gain % = 5 then SP = ?
Calculate figure –> 100& 105
SP = 50 ×105/100 = 52.5
(B) If CP = 50, loss % = 5 then SP = ?
Calculate figure –> 100& 95
SP = 50 × 95/100 = 47.5
Type 1:
If two articles are sold first article at x% profit and the second article at y% loss, thus making no profit, no loss in the transaction,
Then cost price of the two articles are in the ratio y : x
Proof:Let cost price of two articles is Rs.a and Rs.b respectively.
Then profit on the first article = ax/100 and loss on the second article = by/100
There is no profit or no loss in the bargain. –> ax/100 = by/100 –> ax=by –> a/b = y/x
Example:
1) A man purchased two articles for total cost of Rs.9000. He sold the first article at 15% profit and the second at 12% loss. In the bargain, he neither gained nor lost anything. Find cost price of the first article.
a) Rs. 4000 b) Rs.4500 c) Rs.5000 d) Rs.5500
Solution:
Ratio of cost price of the first and the second article = 12 : 15 = 4: 5
Cost price of the first article = 4/9 ×9000 = Rs.4000
Type 2:
On selling an article for Rs.x, a person earns a% profit. In order to earn b% profit, he must sell the article for Rs.x ×(100+b) / (100+a),
i.e. New selling price = (Old selling price × (100 + Desired profit (in%))/ (100+ Initial profit (in%))
Example:
1) On selling an article for Rs.550, a man gains 10%. What should be the selling price, if desired profit is 20%?
a) Rs.500 b) Rs.600 c) Rs.660 d) Rs.715
Solution:
SP= 550×(100 + 20 / 100 +15)
= 550 × 120/110 = Rs.600
2) Ram sold a cow for Rs.136 and thus lost 15%. At what price he should have sold it to gain 15%?
a) Rs.180 b) Rs.150 c) Rs.200 d) Rs.184
Solution:
New selling price = 136 × (100+15)/(10015)
= 136 × 115/85 = Rs.184
Type 3:
1) Shopkeeper buys 25 tables and 10 chairs for Rs. 7000 sells, table at 10%, chair at 12% profit. If he gets 7740 find CP of table and chair?
Solution:
(If Both Increase by 10% then overall increment will be10% i.e. 10% of 7000/ which is Rs.700. But profit = 740. This extra 40/ is due to 2% of chair)
2% Chair –> 40/
100% C(10) –> 2000
1 chair = 2000/10 = 200
So all table (25) = 5000/
1 table = 5000/25 = 200/
Type 4:
If price of an article is marked x% above the cost price and x% discount is allowed on its marked price, thenlosspercent = x^{2}/100
Example:
1) A shopkeeper mark price of his article 12% above the cost Price and then allows 12% discount on the mark price. What is his loss percent?
a) 0% b) 1% c) 1.44% d) 2.4%
Solution:
Loss% = 12^{2}/100 = 1.44%
Type 5:
If two articles are sold for the same selling price. On selling first article, a man gains x% and on selling the other article he loss x%, in such casesthere will be always loss, and Loss% = x^{2}/100 or (Common gain and loss)^{2}/100
Example:
1) A TV manufacturer sells two televisions at Rs.9900 each. He earned a profit of 10% on the first one and suffered 10% loss on another. His net profit or loss percent is?
a) 1% loss b) 1% gain c) 2% loss d) No profit/loss
Solution:
Loss% = (Common gain and loss)^{2}/100
= 10^{2}/100 = 1%
Type 6:
If two articles are sold for the same selling price. On selling the first, the gain is x% and on selling the second the gain is y%, then net % profit
= (2× (100+x) (100+y)/ (100+x) + (100+y)) – 100
Example:
1) A man sold two articles for Rs.600 each. On selling first, he gains 20% and on the other, he gains 30%. What is profit percent in the transaction?
a) 24.8% b) 25% c) 50% d) 56%
Solution:
Profit% = (2×120×130 / 120+130)100 = 24.8%
Type 7:
1) A shopkeeper buys 2 chair at total cost 900/. By selling one at 4/5 of its cost and other at 5/4 of its cost he made a profit 90/. Find CP of each chair
Solution:
4/5 = 80% i.e.20%loss
5/4 = 125% i.e = 25% profit
Profit = 90/ i.e 10% (90 is 10% of 900)
i.e Ratio of their CP = 15 : 30 = 1:2
1^{st}chair = Rs. 300, 2^{nd} chair = Rs. 600/
Type 8:
1) A man purchase 11 orange for Rs.10/ and sell them at the rate of 10 oranges for Rs.11/. Find profit?
Solution:
Profit = (11×11 – 10×10 / 10×10)×100%
= 21%
Type 9:
1) Selling price of two articles 4000/ each. First article sold at profit of 25% profit and 2^{nd} article at some % loss. Find loss % on 2^{nd}article if there is neither loss nor gain.
Solution:
Type 10:
1) How much % more than CP must a shopkeeper mark his goods to gain 26% after giving a discount of 10%
Solution:
=100×126/100×100/90
=140
Difference =140 100 =40%
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