Question

a women has Rs 10,000 with her. she calculated that she could spend Rs x everyday on her holiday. she spent Rs (x–50) everyday and extended holiday for 10 days. find x

Answer 1

Hi ,

Amount Tourist has = Rs 10000

If he spend Rs x each day

Let the number of days he spent 

Rs 10000 = y

Now ,
xy = 10000 -------( 1 )

If he spends Rs ( x - 50 ) , the numberof days he spends the same 

amount = ( y + 10 )

( x - 50 ) ( y + 10 ) = 10000 
xy + 10x - 50y - 500 = 10000 

10000 + 10x - 50y - 500 = 10000

10x - 50y - 500 = 0

Divide each term with 10 we get

x - 5y - 50 =0

x = 5y + 50 ----( 2 )

Put x value in ( 1 )

( 5y + 50 ) y = 10000

5 y^2 + 50y = 10000

Divide each term with 5

y^2 + 10y - 2000 = 0

y^2 - 40y +50y -2000 =0

y ( y - 40 ) + 50 ( y - 40 ) = 0

( y - 40 ) ( y + 50 ) = 0

y - 40 = 0 or y + 50 = 0

y = 40 or y = -50

y should not be negative 

y = 40

Put y value in ( 1 )

x × 40 = 10000

x = 10000/ 40

x = 1000/4

x = 250

Hope This helps :)