PROBLEM & SOLUTION
Example.1) The marked price of a pair of wardrobe is $ 800
1) If it is sold for $ 500, then find the discount and percentage of discount.
2) If it is sold at a discount of 12%, then find the discount and selling price.
1)
Ans.) As per the given condition -
Discount = MP – SP = $ 800 - $ 500 = $ 300
So, the percentage of discount -
Discount
= --------------------- X 100
Marked Price (MP)
$ 300
= ------------- X 100
$ 800
= 37.5 % ………………………………. (1) (Ans.)
2) As per the given condition -
If he sold the pair of product for the percentage of 12%
So, the given discount amount is =
12
$ 800 X --------- = $ 96
100
So, the obtained discount price is $ 96
And the sell price (SP) is = $ 800 - $ 96
= $ 704 …………………………(2) (Ans.)
Example.2) The marked price of a toy is $ 400. The shopkeepers offer a discount of 10% and still makes a profit of 15%, find the selling price (SP) & cost price (CP)
Ans.) Given, Marked Price (MP) = $ 400 and Discount = a = 10
a
Sell Price (SP) = ( 1 - --------- ) X Marked Price (MP)
100
10
= ( 1 - --------- ) X $ 400
100
9
= --------- X 400 = $ 360
10
Now, SP = $ 360 and, Profit = r = 15
r
Sell Price (SP) = ( 1 + -------- ) X Cost Price (CP)
100
15
So, $ 360 = ( 1 + --------- ) X CP
100
3
So, $ 360 = ( 1 + -------- ) X CP
20
23
So, -------- CP = $ 360
20
20
So, CP = $ 360 X --------- = $ 313.04 = $ 313
23
So, the cost price of the product is $ 313 (Ans.)
Example.3) A shopkeepers marks his goods at 40% above the cost price and allows a discount of 10%. Find his percentage profit.
Ans.) Suppose the cost price of the said product is ‘A’
40 2A
Marked Price = A + A X --------- = A + --------- 100 5
5A + 2A 7A
= ------------ = ---------
5 5
Now he is giving a discount of 10% from marked price, so the Sell price (SP) would be –
7A 7A 10
--------- - ( -------- X -------- )
5 5 100
7A 7A 70A – 7A
= --------- - ---------- = --------------
5 50 50
63A
= ----------
50
63A
Profit would be = SP – CP = --------- - A
50
= -----------
50
Now we have to find out the percentage of profit –
At the cost price of A he does profit about 13A/50
Cost price of 1 he does the profit
= --------- X --------- = ----------
50 A 50 13
Cost price of 100 he does the profit = --------- X 100 50
= 26%
So the required percentage of profit is 26%. (Ans.)
Example.4) A trader marks an article such that after allowing a discount of 10%, he still makes a profit of 25%. By what percent is the marked price above the cost price?
Ans.) As per the given condition, suppose cost price (CP) of the article = $ 100
And he has done the profit about = 25% of CP
So, he has done the profit = $ 25
So the sell price = CP + Profit
= $ 100 + $ 25 = $ 125
He has given a discount = 10 %
Suppose the marked price is A
So, as per the requirement –
A - ( A X ------- ) = $ 125
100
A
A - -------- = $ 125
10
10A - A
------------- = $ 125
10
$ 125 X 10
A = --------------- = $ 138.88 = $ 139
9
Now, the obtained mark price is = $ 139
And, the cost price is = $ 100
So, the difference = MP – CP
= $ 139 - $ 100 = $ 39
Now, the percentage is the marked price above the cost price –
$ 39
----------- = 39 %
$ 100
So, the percentage of marked price above the cost price is 39%
(Ans.)
Example.5) Find a single discount equivalent to two successive discounts of 20% & 25%
Ans.) Let a single discount of A% be equivalent to the two successive discounts, then SP after a discount of A% = SP after the two successive discounts of 20% and 25%
A 20 25
So, ( 1 - ------ ) X MP = ( 1 - ------- ) X ( 1 - ------- ) X MP
20 100 100
100 – A 100 – 20 100 - 25
So, ----------- = ( ----------- ) X ( ------------ )
100 100 100
100 – A 80 75
So, ------------ = ---------- X ----------
100 100 100
80 X 75
So, 100 – A = -------------
100
So, 100 – A = 60
A = 100 – 60
A = 40 = 40%
So, the obtained single equivalent discount would be 40% (Ans.)