Question

A certain amount is equal distributed among certain number of students each would get 22 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:

Let the number of students be x and amount given to each student be Rs.y.

:. Total amount distributed is xy

From the first condition we get,

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

- 2x+10y 20 = xy

- 2x + 10y = 20

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

From the 2nd condition we get,

(x - 15) (v + 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 (1)

- x + 5y = 10

:.- 40 + 5y = 10 5y = 50

y = 10

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

400 distributed equally among 40 students.