Samina spent 1\8 of her money to buy books ,1\5 to buy clothes or 1\10 give to charity, if she had still rupees 15 ,more than half of her money ,find the amount she originally had
If she started out with x, and was left with 15 more than half of what she started with, then
x - x/8 - x/5 - x/10 = x/2 + 15
x = 200
Same as
Let's assume the original amount of money Samina had is represented by "x".
According to the given information:
- She spent 1/8 of her money on books, which is (1/8)*x.
- She spent 1/5 of her money on clothes, which is (1/5)*x.
- She gave 1/10 of her money to charity, which is (1/10)*x.
She had rupees 15 more than half of her money left, which is (1/2)*x + 15.
Since the amount left is given as 15 more than half of her money, we can set up the equation:
(1/2)*x + 15 = (1/2)*x + 15
To find the original amount she had (x), we need to solve this equation.
(1/8)*x + (1/5)*x + (1/10)*x + (1/2)*x + 15 = x
Combining like terms gives us:
(13/40)*x + (1/2)*x + 15 = x
Multiplying through by the common denominator (40) gives us:
13x + 20x + 600 = 40x
Combining like terms gives us:
33x + 600 = 40x
Subtracting 33x from both sides gives us:
600 = 7x
Dividing both sides by 7 gives us:
x = 85
So, the original amount of money Samina had was 85 rupees.
To find the amount Samina originally had, we'll work backward based on the information provided.
Let X be the original amount of money Samina had.
She spent 1/8 of her money on books, which is (1/8)X.
She spent 1/5 of her money on clothes, which is (1/5)X.
She gave 1/10 of her money to charity, which is (1/10)X.
So, the amount she spent and gave away is:
(1/8)X + (1/5)X + (1/10)X = (13/40)X
We are also told that she had Rs.15 more than half of her money left. Half of her money is (1/2)X, and if she had Rs.15 more than that, it can be represented as (1/2)X + 15.
According to the information provided, the remaining amount is more than half her money:
(13/40)X > (1/2)X + 15
To solve this inequality and find the range of X, we can subtract (1/2)X from both sides and simplify:
(13/40)X - (1/2)X > 15
(13/40 - 20/40)X > 15
(-7/40)X > 15
To get rid of the negative sign on the left side, we multiply both sides by -1 (which flips the direction of the inequality):
(7/40)X < -15
Finally, to solve for X, we divide both sides by (7/40):
X < (-15) / (7/40)
Using a calculator, this evaluates to:
X < -85.714
Therefore, the original amount Samina had is any value less than -85.714. However, since this doesn't make sense in the context of money, we can conclude that there is no valid solution based on the given information.