Question

The cost price of 16 books as equal to the
selling price of 30 books. Find the gain percentage​

Answer 1

First of all, you have mistaken to type the question.

The correct question is,

The cost price of 16 books as equal to the  selling price of 30 books. Find the gain or loss percentage.

                                     or,

​The cost price of 16 books as equal to the  selling price of 30 books. Find the loss percentage​.

So, now let's do the calculations:

While the cost price of 16 books is equal to that of the selling price of 30 books so, it can be concluded that there is a loss as, the cost price is more than the selling price and while the cost price is more than the selling price then there might be a loss.

Let, the cost price of 1 book be, 'n'

So, the cost price of 16 books = (n×16)

                                                 = 16n

∴ The cost price of 30 books = (n×30)

                                                = 30n

As per the question the selling price of 30 books is 16n.

Loss = (Cost price - selling price)

∴ Loss = (30n-16n)

           = 14n

∴ Loss% = (14n × 100)/16n

              = (7×100)/8

              = (7×25)/2

             = 175/2

             = 87.5 %

∴ The loss is 87.5 %.

Answer 2

46.67 % Loss if cost price of 16 books as equal to the  selling price of 30 books  and 87.5 % gain if cost price of 30 books as equal to the  selling price of 16 books

Step-by-step explanation:

Correct Question would be either

The cost price of 16 books as equal to the  selling price of 30 books. Find  loss percentage.

                                    or,

​The cost price of 30 books as equal to the  selling price of 16 books. Find the Gain percentage​.

Case 1 :

Let say Cost Price of 1 book  = C

Selling Price of 1 book  = S

Cost Price of 16 books = 16C

Selling Price of 30 Books = 30S

16C = 30S

=> S = 8C/15

Loss = C - 8C/15  = 7C/15

Loss%  =  100 * (7C/15) /C

= 140/3 %

= 46.67 % Loss

Case2 :

Cost Price of 30 books = 30C

Selling Price of 16 Books = 16S

16S = 30C

=> S = 15C/8

Profit  = 15C/8 - C  =  7C/8

Profit %  =  100 * (7C/8)/C

= 175/2

= 87.5 %

Gain % = 87.5 %

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