Question

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A shopkeeper buys a number of books for rupees 1200. If he had bought 10 more books for the same amount, each book would have cost 20 rupees less. How many books did he buy?

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Answer 1

Answer:

let the shopkeeper bought x number of books for Rs.1200 

price for each book = 1200/x 

If he had bought 10 more books for the same amount each book would have cost Rs 20 less

it means 

the cost of each books is decreased by 20 if he had bought 10 more books 

I.e.

ATQ 

1200/x - 1200/x + 10 = 20 

1200(1/x - 1/(x+10)   = 20 

1/x - 1/x+10              = 20/1200 

(x+10) - x /x(x+10)    = 1/60 

x+10 -x                     = x² + 10x / 60 

600                           = x² + 10x 

x² + 10x - 600           = 0 

Here quadratic equation formed ...

x² + 10x - 600           = 0 

x² + 30x - 20x - 600  = 0 

x(x+30) -20(x+30)     = 0 

(x+30) (x-20)             = 0 

either 

(x+30) =0 or (x-20) = 0 

x = -30 or x = 20 

x = -30 X not possible because the number of books cant be negative 

so number of books = x = 20

I'll have another method in an attachment