Question

Thomas bought x number of sports goods for rs.12000. If each item was cheaper by rs.30 then with the same amount he could have bought 50 more items than x. Find the number of items bought by thomas ?

Answer 1

Answer:

between 118 & 119

Step-by-step explanation:

Thomas bought x number of sports goods for rs.12000

=> Price of item = 12000/x

if each item was cheaper by rs.30

Price of item = 12000/x - 30

he could have bought 50 more items than x

=> items = ( x + 50)

Total Price = (12000/x - 30) (x + 50)  = 12000

=>( 12000 - 30x)(x + 50) = 12000x

=>  (400 - x)(x + 50) = 400x

=> -x² + 400x - 50x + 20000 = 400x

=> x² + 50x - 20000 = 0

=> x does not comes an integer

but between 118 & 119

Answer 2

Answer:

118 or 119

Step-by-step explanation:

Let the number of sports goods bought by Thomas = x

Total price of x item = Rs 12000

Therefore,

Price of one item = 12000/x

If each item was cheaper by Rs.30, then

New price of each item $\frac{1200}{x}-30$

But he bought 50 items more, that is

Total number of items = x + 50

Total cost of (x+50) items

$(\frac{12000}{x}-30) \times (x+50)$

Now,

$(\frac{12000}{x}-30) \times (x+50)= 12000$

On solving this equation, we get

$x^{2} +50x-20000$

As we know that x is a number of items which can not be expressed in fraction.

Hence,  the number of items bought by thomas is either 118 or 119.