A school spends a quator of it's money on books and a third on salaries. If the school spends a fifth of the remainder on transport, the remainig amount was sh.40,000. How much money did the school have at first?
1 - 1/4 - 1/3 = 5/12
1/5 of that is 1/12
So, 1/12 of the original amount is 40,000
To solve this problem, we can work backwards.
Let's assume the amount of money the school had at first is "X".
The school spends a quarter (1/4) of its money on books, which is (1/4)X.
The school spends a third (1/3) of its money on salaries, which is (1/3)X.
So, the remaining amount after spending on books and salaries is: X - (1/4)X - (1/3)X.
Simplifying this expression gives us: (12/12)X - (3/12)X - (4/12)X = (5/12)X.
It is given that the school spends a fifth (1/5) of the remainder on transport, so the amount spent on transport is: (1/5) * (5/12)X = (1/12)X.
The remaining amount after spending on books, salaries, and transport is: (5/12)X - (1/12)X.
According to the given information, this remaining amount is 40,000 shillings.
Therefore, we can set up an equation: (5/12)X - (1/12)X = 40,000.
Simplifying the equation gives us: (4/12)X = 40,000.
To solve for X, we multiply both sides of the equation by 12/4, giving us: X = 40,000 * (12/4).
Calculating this gives us: X = 120,000.
Therefore, the school had 120,000 shillings at first.