Question

Amrita bought some pens for Rs 360. When the price was reduced by Rs 3, she could buy 6 more pens for the same cost of Rs360. Find the original cost of the pen​

Answer 1

Answer:

Step-by-step explanation:

let,no of pen is x

and cost of pen is y

from the first condation

xy=360

from the sec cond

(y-3)(6+x)=360

y(6+x)-3(6+x)=360

6y +xy-18-3x =360

put xy=360

6y+360-18-3x=360

6y+ 342-3x=360

-3x+6y=18 take 3 common

-x+y=6

put x=360/y

-360/y+y=6

y=6y/360

Answer 2

Answer:

no. of pens she bought = x

Rs. = 360

Cost 1 = 360/x

No. of pens she could have bought = x + 6

Rs. = 360

Cost 2 = 360/( x + 6 )

C 1 is greater than C 2 by 3

C1 = C2+3

$\frac{360}{x} = \frac{360}{x + 6} + 3$

$\frac{360}{x} - \frac{360}{x + 6 } = 3$

$360( \frac{1}{x} - \frac{1}{x + 6} ) = 3$

$360( \frac{x + 6 - x}{ {x}^{2} + 6x }) = 3$

$\frac{360 \times 6}{ {x}^{2} + 6x} = 3$

$2160 = 3 {x}^{2} + 18x$

$3 {x}^{2} + 18x - 2160 = 0$

${x}^{2} + 6x - 720 = 0$

${x}^{2} + 30x - 24x - 720 = 0$

$x(x + 30) - 24(x + 30) = 0$

$(x + 30)(x - 24) = 0$

x = -30 x = 24

No. of pens she bought is 24.

Cost = 360/24

= 60/4

= 15 rs.