# CLASS-8DISCOUNT-PROBLEM & SOLUTION

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

13A

= -----------

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

13A            1              13

= --------- 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 –

10

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.)