Question

A Shopkeeper gives 5 articles free on the purchase of every 15
articles. He also allow a discount of 20% to customer and still earn
20% profit. Find the ratio of the cost price to the marked price of
the article?
1:2
1:3
2:1
1:4​

Answer 1

Answer:

The ratio of Cost Price to Marked price is 1 : 2.

Step-by-step explanation:

Given :

5 articles free on = purchase of every 15 articles

To find :

Ratio of CP to MP

Solution :

Let Cost Price be Rs. 100

The shopkeeper allows a discount of 20%,

Cost Price = 100 - 20% of 100

                      = 100 - 20

                      = Rs. 80

Total articles sold = 15 + 5

                                       = 20

$\rule{300}{1.5}$

Cost Price of one Article = 80/20

                                                  = Rs. 4

$\rule{300}{1.5}$

Profit made of 20%,

Marked Price = 100 + 20% of 100

                             = 100 + 20

                             = Rs. 120

Number of articles which are charged = 15

Marked Price of one article = 120/15

                                                = Rs. 8

$\rule{300}{1.5}$

Ratio of CP to MP,

• Cost Price = Rs. 4
• Marked Price = Rs. 8

CP : MP = 4 : 8

CP : MP = 1 : 2

$\therefore$ The ratio of Cost Price to Marked price is 1 : 2.

Answer 2

||✪✪ QUESTION ✪✪||

A Shopkeeper gives 5 articles free on the purchase of every 15 articles. He also allow a discount of 20% to customer and still earn 20% profit. Find the ratio of the cost price to the marked price of the article?

1:2

1:3

2:1

1:4

|| ✰✰ ANSWER ✰✰ ||

Given That, The Shopkeeper gives 5 articles free on the purchase of every 15 articles.

That Means ,

→ He is Giving a Discount of = (Free items) * 100/ (Total items The buyer Bought ).

→ Discount % = (5*100)/20 = 25% .

__________________________

Now, Also Given That, He also allow a discount of 20% to customer .

So,

→ Overall Discount % The shoppkeeper is giving is = (20 + 25) - (20*25/100)

→ Overall Discount % = 20 + 25 - 5 = 40% .

_________________________

Now, we have Overall Discount % Shopkeeper give is 40% and Still he Earn a profit of 20% .

we know That, now, Relation between Cost price and Marked is :-

☛ CP : MP = (100 - Discount %) : (100 + Profit%)

So,

☞ CP : MP = (100 - 40) : (100 + 20)

☞ CP : MP = 60 : 120

☞ CP : MP = 1 : 2.

Hence, the ratio of the cost price to the marked price of the article is 1:2.