Question

A certain amount is equally distributed among certain number of students.

Each would get ` 2 less if 10 students were more and each would get 6 more if 15 students were less. Find the number of students and the

amount distributed.​

Answer 1

Answer:

X students and each can be given Y rupees.

Now,

Each would get rs. 2 less if 10 students were more => (X+10) students would get each (Y-2)

Amount= (X+10)*(Y-2)

Each would get rs. 6 more if 15 students were less=> (X-15) students would get each (Y+6)

Amount= (X-15)*(Y+6)

(X+10)*(Y-2)=(X-15)*(Y+6)

XY-2X+10Y-20=XY+6X-15Y-90

8X-25Y=70. eq1

Similarly

XY=(X+10)*(Y-2)

XY=XY-2X+10Y-20

2X-10Y=-20.

2X*4–10Y*4=-80 Eq2

Using eq1 and 2

X=40

Y=10

Answer 2

.$\bf\large\underline\green{Answer:-}$

Solution : Let the number of students be x and amount given to each student

be ` y.

Total amount distributed is xy

From the first condition we get,

(x + 10) (y - 2) = xy

xy - 2x + 10y - 20 = xy

- 2x + 10y = 20

- x + 5y = 10 . . . (I)

From the 2nd condition we get,

(x - 15) (y + 6) = xy

xy + 6x - 15y - 90 = xy

6x - 15y = 90

2x - 5y = 30 . . . (II)

Adding equations (I) and (II)

- x + 5y = 10

2x - 5y = 30

x = 40

Substitute this value of x in equation (I)

- x + 5y = 10

- 40 + 5y = 10

5y = 50

y = 10

Total amount distributed is = xy = 40 ´ 10 = ` 400.

` 400 distributed equally among 40 students.