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Collection of online calculators which will help you to solve mathematical problems with their step by step solution at just a mouse click.
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Profit Loss Discount
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Problem 1 of 21
1. Find selling price when cost price = Rs.
, Loss/Gain =
% .
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Profit Loss Discount
This is sample question and answer for help purpose.
1. Find selling price when cost price = Rs. 50 , Loss/Gain = 10 % .
`"C.P." = "Rs." 50," Gain" = 10%`
`"S.P." = "C.P." × (100 + "Gain"%) / 100 = 50 × (100 + 10) / 100 = 55 " Rs."`
`"C.P." = "Rs. " 50," Loss" = 10%`
`"S.P." = "C.P." × (100  "Loss"%) / 100 = 50 × (100  10) / 100 = 45 " Rs."`
Problem :
1
/
21
[ Profit Loss Discount ]
Solve this type of problem
1
. Find selling price when cost price = Rs. 50 , Loss/Gain = 10 % .
Solution:
`"C.P." = "Rs." 50," Gain" = 10%`
`"S.P." = "C.P." × (100 + "Gain"%) / 100 = 50 × (100 + 10) / 100 = 55 " Rs."`
`"C.P." = "Rs. " 50," Loss" = 10%`
`"S.P." = "C.P." × (100  "Loss"%) / 100 = 50 × (100  10) / 100 = 45 " Rs."`
Problem :
2
/
21
[ Profit Loss Discount ]
Solve this type of problem
2
. Find cost price when selling price = 55 , Loss/Gain = 10 %
Solution:
`"S.P." = "Rs. "55," Gain" = 10%`
`"C.P." = "S.P." × 100/(100 + "Gain"%) = 55 × 100/(100 + 10) = 50 " Rs."`
`"S.P." = "Rs. "55," Loss" = 10%`
`"C.P." = "S.P." × 100/(100  "Gain"%) = 55 × 100/(100  10) = 61.1111 " Rs."`
Problem :
3
/
21
[ Profit Loss Discount ]
Solve this type of problem
3
. Find Loss/Gain % when cost price = 50 and selling price = 55 .
Solution:
`"C.P." = "Rs. "50," S.P." = "Rs. "55`
`"Gain" = "S.P."  "C.P." = 55  50 = "Rs. "5`
`"Gain" % = ("Gain" × 100)/("C.P.") = (5 × 100)/50 = 10%`
`"C.P." = "Rs. "50," S.P." = "Rs. "55`
`"Loss" = "C.P."  "S.P." = 50  55 = "Rs. "5`
`"Loss" % = ("Loss" × 100)/("C.P.") = (5 × 100)/50 = 10%`
Problem :
4
/
21
[ Profit Loss Discount ]
Solve this type of problem
4
. By selling an article for Rs 110 a man loses 12 %. For how much should he sell it to gain 8 %.
Solution:
Here `"S.P." = "Rs. "110," Loss" = 12%`
`"C.P." = "S.P." × 100/(100  "Loss"%) = 110 × 100/(100  12) = 125" Rs."`
Now, `"C.P." = "Rs. "125," Gain" = 8%`
`"S.P." = "C.P." × (100 + "Gain"%)/100 = 125 × (100 + 8)/100 = 135" Rs."`
Problem :
5
/
21
[ Profit Loss Discount ]
Solve this type of problem
5
. A man sells two houses for Rs 536850 each. On one he gains and on the other he loses 5 %. Find his gain or loss % on the whole transaction.
Solution:
In such a problem selling price is not neccessary.
There is always a loss given by
Loss % = `(( text{Common Gain or Loss } %)/10)^2 = (5/10)^2 = 0.25` %
Problem :
6
/
21
[ Profit Loss Discount ]
Solve this type of problem
6
. If selling price of 10 articles is the same as the cost price of 12 articles, find the gain %.
Solution:
Let C.P. of each article be Rs. `1`
C.P. of `10` articles = Rs. `10`
S.P. of `10` articles = Rs. `12`
`:.` Gain % `= ("Gain" × 100)/("C.P.") = (2 × 100)/10 = 20` %
Problem :
7
/
21
[ Profit Loss Discount ]
Solve this type of problem
7
. By selling 100 pencils, a shopkeeper gains the selling price of 20 pencils. Find the gain percent.
Solution:
(S.P. of `100` pencils)  (C.P. of `100` pencils) = S.P. of `20` pencils.
`:.` S.P. of `80` pencils = C.P. of `100` pencils
Let C.P. of each pencil be Rs. `1`
C.P. of `80` pencils = Rs. `80`
S.P. of `80` pencils = Rs. `100`
`:.` Gain % `= ("Gain" × 100)/("C.P.") = (20 × 100)/80 = 25` %
Problem :
8
/
21
[ Profit Loss Discount ]
Solve this type of problem
8
. A dishonest dealer professes to sell his goods at cost price but uses a weight of 960 grams for 1000 grams. Find the gain percent.
Solution:
Here Gain = price of `40` grams and C.P. = price of `960` grams
Gain % `= ("Gain" × 100)/("C.P.") = (40 × 100)/960 = 4.1667` %
Problem :
9
/
21
[ Profit Loss Discount ]
Solve this type of problem
9
. If the marked price of an article is Rs. 380 and a discount of 5 % is given on it, what is the selling price ?
Solution:
Here marked price = Rs. `380` and discount = `5` %
S.P. = `95` % of Rs. `380 = 95/100 × 380 = 361` Rs.
Problem :
10
/
21
[ Profit Loss Discount ]
Solve this type of problem
10
. If 12 % is allowed as discount on a radio and its selling price is Rs. 836 , what is its marked price ?
Solution:
Here discount = `12` % and S.P. = `836`
Let Marked Price = Rs. X
`88` % of X = `836`
`:. X = 836 × 100/88`
`:. X = 950`
`:.` Marked Price = Rs. `950` .
Problem :
11
/
21
[ Profit Loss Discount ]
Solve this type of problem
11
. A cycle dealer marks his goods 25 % above his cost price and allows a discount of 8 % on it. Find his gain percent.
Solution:
Let C.P. = Rs. `100`.
Then, marked price = Rs. `(100 + 25` % of `100)` = Rs. `125`
S.P. = `92` % of `125` = Rs. `115`
Gain = S.P.  C.P. = `115  100 = 15`
Gain% = `15` %
Problem :
12
/
21
[ Profit Loss Discount ]
Solve this type of problem
12
. Successive discounts of 20 % and 10 % equivalent to a single discount of how many percent?
Solution:
Let marked price = Rs. `100` S.P.
After first discount = `80` % of `100` S.P.
After second discount = `90` % of `80` % of `100` = Rs. `72` .
This is equivalent to a single discount of `( 100  72 ) % = 28 %`.
Problem :
13
/
21
[ Profit Loss Discount ]
Solve this type of problem
13
. If a commission of 10 % is given on the list price, the gain is 20 %. Find the gain percent, if the commission is increased to 20 %.
Solution:
Let list price = Rs. `100`, commission = `10` % and gain = `20` %
`:. "S.P." = "Rs." 90`
`:. "C.P." = 100/120 × 90` = Rs. `75`
Now if commission = `20` %, Then
New S.P. = Rs. `80`
New Gain % = `(5/75 × 100) % = 6.6667 %`
Problem :
14
/
21
[ Profit Loss Discount ]
Solve this type of problem
14
. If the manufacturer gives 20 % commission to the dealer on the printed price and if the dealer sells the item at the printed price, what is the percentage of his profit ?
Solution:
Let the printed price be Rs `100`
manufacturer gives `20` % commission to the dealer on the printed price, i.e. commission is Rs `20`
`:.` dealer will pay Rs `( 100  20 )` = Rs `80` for the printed price Rs `100`
And now it sells it at printed price, so the sales price is Rs `100` and the cost price is Rs `80`
`:.` Profit `= "S.P."  "C.P." = 100  80 = 20`
C.P.
Profit
80
20
100
?
Profit = `20 × 100/80 = 25 %`
`:.` the profit is `25` %
Problem :
15
/
21
[ Profit Loss Discount ]
Solve this type of problem
15
. A dealer gets 25 % commission on the printed price of an item. If he gives 10 % discount to the customer on printed price, find his prifit in percentage.
Solution:
Let the pritned price be Rs `100`
A dealer gets `25` % commission on the printed price of an item
Amount paid by the dealer = printed price  commision = `100  25 = 75`
Now he gives `10` % discount to the customer on printed price
Amount paid by customer = printed price  discount `= 100  10 = 90`
That means dealer purchase it for Rs `75` and sells it for Rs `90`
`:.` proit `= "S.P."  "C.P." = 90  75 = 15`
C.P.
Profit
75
15
100
?
Profit = `15 × 100/75 = 20 %`
`:.` the profit is `20` %
Problem :
16
/
21
[ Profit Loss Discount ]
Solve this type of problem
16
. The printed price of a saree is Rs 900 . A clothmearchant purchases it at 15 % commission. He spends Rs 35 for rollpolish and then sells the saree at the printed price. What is the prifit of the merchant in percentage ?
Solution:
A clothmearchant purchases a saree at `15` % commission
Purchase Price = Printed price  commission `= 100  15 = 85`
Printed Price
Purchase Price
100
85
900
?
Purchase price = `85 × 900/100 = 765`
The Purchase price = `765`
C.P. = purchase price + other expenses `= 765 + 35 = 800`
S.P. = printed price = Rs `900`
Profit `= "S.P."  "C.P." = 900  800 = 100`
Problem :
17
/
21
[ Profit Loss Discount ]
Solve this type of problem
17
. A carpenter made a table which cost him Rs 1500 . He decided the price so that he would get 20 % profit. He gave 8 % commission on the decided price while selling. Find the sales price of the table and the profit of the carpenter.
Solution:
A carpenter decided the price so that he would get `20` % profit
Decided Price = C.P. + Profit `= 100 + 20 = 120` .
C.P.
Decided Price
100
120
1500
?
Decided price = `120 × 1500/100 = 1800`
`:.` Decided price = `1800`
He gave `8` % commission on the decided price
S.P. = Decided price  commission `= 100  8 = 92`
Decided Price
S.P.
100
92
1800
?
S.P. = `92 × 1800/100 = 1656`
`:.` the sales price is Rs `1656`
Profit `= "S.P."  "C.P." = 1656  1500 = 156`
`:.` Profit is Rs `156`
C.P
Profit
1500
156
100
?
Profit = `156 × 100/1500 = 10.4`
`:.` the sales price of the table is Rs `1656` and the profit of carpenter is `10.4` %
Problem :
18
/
21
[ Profit Loss Discount ]
Solve this type of problem
18
. The printed price of a book is Rs 720 . After giving 10 % discount to the customer on the printed price, the bookseller gets 20 % profit. Find the purchase price for the bookseller.
Solution:
The printed price of a book is Rs `720`.
After giving `10` % discount to the customer on the printed price
S.P. = Printed price  discount `= 100  10 = 90`
Printed Price
S.P.
100
90
720
?
the bookseller gets `20` % profit,
S.P. = C.P. + Profit `= 100 + 20 = 120`
S.P.
C.P.
120
100
648
?
C.P. = `100 × 648/120 = 540`
The purchase price for the book seller is Rs `540`.
Problem :
19
/
21
[ Profit Loss Discount ]
Solve this type of problem
19
. If 20 % discount is given on the decided price which is decided by addition of 20 % profit on the purchase price, then will there be profit or loss? What is the percentage?
Solution:
Decided price is `20` % profit on the purchase price
Decided price = purchase price + profit `= 100 + 20 = 120`
`20` % discount is given on the decided price
Discount = `20` % of decided price = `20` % of `120 = 20/100 × 120 = 24`
The discount is Rs `24`
S.P. = decided price  discount `= 120  24 = 96`
Loss = Purchase Price  Selling Price `= 100  96 = 4`
Hence there will be `4` % Loss in this case.
Problem :
20
/
21
[ Profit Loss Discount ]
Solve this type of problem
20
. A watch manufacturing company decided the price with 25 % profit on the cost price. By selling a watch with 8 % discount on th printed price, the company has a profit of Rs 300 . Find the costprice of a watch.
Solution:
A watch manufacturing company decided the price with `25` % profit on the cost price
Printed price = C.P. + profit `= 100 + 25 = 125`
By selling a watch with `8` % discount on th printed price
S.P. = C.P.  discount `= 100  8 = 92`
C.P.
S.P.
100
92
125
?
S.P. `= 92 × 125/100 = 115`
Profit = S.P.  C.P. `= 115  100 = 15`
Profit
C.P.
15
100
300
?
`C.P. = 100 × 300/15 = 2000`
`:.` the cost price is Rs `2000`.
Problem :
21
/
21
[ Profit Loss Discount ]
Solve this type of problem
21
. If the sales price of 12 pens is fixed as the original price of 15 pens, then what percentage of profit is earned in the deal ?
Solution:
Let the original price of `1` pen be Rs `1`
`:.` original price of `12` pen be Rs `12`
Also selling price of `12` pens = original price of `15` pens = Rs `15`
Profit `= "S.P."  "O.P." = 15  12 = 3`
Original Price
Profit
12
3
100
?
Profit `= 3 × 100/12 = 25`
`:.` the profit is `25` %
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