Four people share a sum of money the first takes 1/6 the second takes 2/5 the third takes 3/10 there is 240 dh left for the fourth what is the amount of the sum of money what is the share of each one
Let's assume the sum of money is 'x'.
The first person takes 1/6 of the money, which is (1/6)x.
The second person takes 2/5 of the money, which is (2/5)x.
The third person takes 3/10 of the money, which is (3/10)x.
The total amount taken by the first three people is (1/6)x + (2/5)x + (3/10)x.
Therefore, the amount left for the fourth person is x - [(1/6)x + (2/5)x + (3/10)x] = 240.
Simplifying this equation, we get:
x - [(1/6)x + (2/5)x + (3/10)x] = 240
x - [(5/30)x + (12/30)x + (9/30)x] = 240
x - [(26/30)x] = 240
(4/30)x = 240
(2/15)x = 240
x = (240 * 15) / 2
x = 1800.
Therefore, the sum of money is 1800 dh.
Now, let's find the share of each person.
The first person's share = (1/6) * 1800 = 300 dh.
The second person's share = (2/5) * 1800 = 720 dh.
The third person's share = (3/10) * 1800 = 540 dh.
The fourth person's share = 240 dh (given).
So, the share of each person is:
First person: 300 dh
Second person: 720 dh
Third person: 540 dh
Fourth person: 240 dh