A distributes Rs.180 equally among a certain number of people. B distributes the same sum but gives to each person Rs. 6 more than A does, and gives the same sum to 40 persons less than A does. How much does A gives to each person?
A:
each gets 180/n = x
so n = 180/x
B: (x+6)(n -40) = 180
(x+6)(180/x - 40) = 180
(x+6)(180 - 40 x ) = 180 x
180 x - 40 x^2 + 1080 - 240 x = 180 x
40 x^2 +240 x -1080 = 0
x^2 + 6x - 27 = 0
(x-9)(x+3) = 0
x = 9 (or - 3 )
number of people that A gives money to ---- n
each person's share = 180/n
number of people that B gives money to ---- n-40
each person's share in B episode = 180/(n-40)
the shares differ by 6 ----> 180/(n-40) - 180/n = 6
multiply each term by n(n-40)
180n - 180(n-40) = 6n(n-40)
7200 = 6n^2 - 240n
Carry on, let me know what answer you get.
Let's assume that A gives Rs. x to each person.
Therefore, the total sum of money A distributes can be expressed as x * n, where n is the number of people.
According to the problem, B gives Rs. 6 more than A does to each person. So, B gives (x + 6) to each person.
Also, B gives the same total sum of money to 40 persons less than A does. Hence, B distributes (n - 40) * (x + 6) amount of money.
Since A distributes Rs. 180 equally, we can write the equation:
x * n = 180
Similarly, B distributes the same sum, so we can write:
(n - 40) * (x + 6) = 180
Now, we can solve these two equations to find the value of x.
Firstly, let's expand the second equation:
nx + 6n - 40x - 240 = 180
By simplifying terms and combining like terms, we get:
nx - 40x + 6n - 240 = 180
Moving the constant terms to the right side:
nx - 40x + 6n = 420
Let's solve this equation for n:
n(x - 40) = 420 - 6n
nx - 40n = 420 - 6n
nx + 6n = 420 + 40n
nx = 420 + 40n - 6n
nx = 420 + 34n
Now, we can substitute the value of x from the first equation into this equation:
180 = 420 + 34n
Subtracting 420 from both sides:
-240 = 34n
Dividing both sides by 34:
n = -240 / 34
n ≈ -7.06
Since the number of people cannot be negative or fractional, we can conclude that there is no real solution to this problem. Please check the given information and conditions again to ensure correctness.
Let's assume that the number of people A distributes the money equally among is 'x'.
According to the given information, A distributes Rs. 180 equally among 'x' people.
So, A gives each person Rs. 180/x.
Now let's consider B. B gives Rs. 6 more to each person than A does. So, B gives each person Rs. (180/x) + 6.
B also distributes the same sum to 40 persons less than A does. This means B distributes the money among (x - 40) people.
Since B distributed the same sum as A, we can set up an equation:
180/x = [(180/x) + 6]*(x - 40)
Now, let's solve this equation to find the value of x, which represents the number of people A distributes the money among.
Expanding the equation, we get:
180 = (180 + 6x - 240)
Simplifying further:
6x = 240
Dividing both sides by 6, we find:
x = 40
Therefore, A distributes Rs. 180 equally among 40 people.
So, A gives each person Rs. 180/40 = Rs. 4.5.