Question

Rani decided to distribute some amount to poor students for their books. If there are 8 students less everyone will get Rs 10 more. if there are 16 students more everyone will get Rs 10 less what is the number of students and how much does each get and what is the total amount distributed ​

Answer 1

Answer:

no of students = 32, total amount = 30

Step-by-step explanation:

let amount of one person be x

let no. of students be y

1 2 3

no of students y y -8 y +16

amount of one person x x +10 x - 10

• yx = total amount
• (y-8)(x + 10) = total amount
• (y + 16) (x - 10) = total amount
• therefore, (y-8)(x+10) = (y+16)(x-10)
• yx -8x +10y -80 = yx + 16x -10y -160
• yx -yx +160 -80 = 16x +8x -10y-10y
• 80 = 24x -20y - equation 1

• yx = (y-8)(x+ 10)
• yx = yx -8x+10y -80
• yx - yx +80 = 10y- 8x
• 80 = 10y - 8x - equation 2
• substituting values from equation 1 and 2
• 10y - 8x = 24x - 20 y
• 10y + 20y = 24x + 8x
• 30y = 32 x
• y = 32/30x - equation 3
• putting values of equation 3 in equation 1
• 80 = 24x - 20( 32/30x)
• 80 = 24 x - 64/3 x
• 80 = 8/3 x
• 80×3/8 =x
• 30 = x - equation 4
• putting values of equation 4 to equation 3
• y = 32 × 30 / 30
• y = 32
• no of students is 32
• total amount = 32 × 30 = 960 rupees.

Answer 2

Answer:

no of students = 32, total amount = 30

Step-by-step explanation:

let amount of one person be x

let no. of students be y

1 2 3

no of students y y -8 y +16

amount of one person x x +10 x - 10

yx = total amount

(y-8)(x + 10) = total amount

(y + 16) (x - 10) = total amount

therefore, (y-8)(x+10) = (y+16)(x-10)

yx -8x +10y -80 = yx + 16x -10y -160

yx -yx +160 -80 = 16x +8x -10y-10y

80 = 24x -20y - equation 1

yx = (y-8)(x+ 10)

yx = yx -8x+10y -80

yx - yx +80 = 10y- 8x

80 = 10y - 8x - equation 2

substituting values from equation 1 and 2

10y - 8x = 24x - 20 y

10y + 20y = 24x + 8x

30y = 32 x

y = 32/30x - equation 3

putting values of equation 3 in equation 1

80 = 24x - 20( 32/30x)

80 = 24 x - 64/3 x

80 = 8/3 x

80×3/8 =x

30 = x - equation 4

putting values of equation 4 to equation 3

y = 32 × 30 / 30

y = 32

no of students is 32

total amount = 32 × 30 = 960 rupees.