A certain amount is equally distributed among certain number of studen

1.	A certain amount is equally distributed among certain number of students. Each would get rs 2 less if 10 students were more and each would get rs 6 more if 15 students were less. Find the number of students and the amount distributed.
Answer» $\huge\underline\frak{\fbox{AnSwEr :-}}$ Let the number of students be x and AMOUNT given to each student be ` y. $\implies$ Total amount distributed is xy From the FIRST condition we get, $\implies$ (x + 10) (y - 2) = xy $\implies$ xy - 2x + 10y - 20 = xy $\implies$ - 2x + 10y = 20 $\implies$ - x + 5y = 10 . . . (I) From the 2nd condition we get, $\implies$ (x - 15) (y + 6) = xy $\implies$ xy + 6X - 15y - 90 = xy $\implies$ 6x - 15y = 90 $\implies$ 2x - 5y = 30 . . . (II) Adding equations (I) and (II) $\implies$ - x + 5y = 10 + 2x - 5y = 30 $\implies$ x = 40 Substitute this value of x in equation (I) $\implies$ - x + 5y = 10 $\implies$ - 40 + 5y = 10 $\implies$ 5y = 50 $\implies$ y = 10 Total amount distributed is = xy = 40 x 10 = rs 400. $\implies$ rs` 400 distributed equally AMONG 40 students.

A certain amount is equally distributed among certain number of students. Each would get rs 2 less if 10 students were more and each would get rs 6 more if 15 students were less. Find the number of students and the amount distributed.

Answer»

$\huge\underline\frak{\fbox{AnSwEr :-}}$

Let the number of students be x and AMOUNT given to each student be ` y.

$\implies$ Total amount distributed is xy

From the FIRST condition we get,

$\implies$ (x + 10) (y - 2) = xy

$\implies$ xy - 2x + 10y - 20 = xy

$\implies$ - 2x + 10y = 20

$\implies$ - x + 5y = 10 . . . (I)

From the 2nd condition we get,

$\implies$ (x - 15) (y + 6) = xy

$\implies$ xy + 6X - 15y - 90 = xy

$\implies$ 6x - 15y = 90

$\implies$ 2x - 5y = 30 . . . (II)

Adding equations (I) and (II)

$\implies$ - x + 5y = 10 + 2x - 5y = 30

$\implies$ x = 40

Substitute this value of x in equation (I)

$\implies$ - x + 5y = 10

$\implies$ - 40 + 5y = 10

$\implies$ 5y = 50

$\implies$ y = 10

Total amount distributed is = xy = 40 x 10 = rs 400.

$\implies$ rs` 400 distributed equally AMONG 40 students.