Gopal spent three fifths of his money in the first week and one third of the remainder in the secondweek.He spent $110 altogether.How much money did he have left?
3/5 x + (1/3)(2/5)x = 110
x = 150
so, he had $40 left.
To find out how much money Gopal had left, we need to work backwards from the amount he spent.
Let's say Gopal had x amount of money initially.
In the first week, he spent three-fifths (3/5) of his money, which can be expressed as (3/5) * x.
After the first week, he has a remainder of (2/5) * x.
In the second week, he then spent one-third (1/3) of the remainder, which can be expressed as (1/3) * (2/5) * x.
So, the total amount Gopal spent is:
(3/5) * x + (1/3) * (2/5) * x = $110.
To solve this equation for x, we can simplify it:
(3/5) * x + (2/15) * x = $110.
Now, we can find a common denominator and combine the terms:
(9/15) * x + (2/15) * x = $110.
(11/15) * x = $110.
Next, isolate x by multiplying both sides of the equation by the reciprocal of (11/15), which is (15/11):
x = ($110 * (15/11)).
Evaluating this expression, we find that x is approximately $150.
Therefore, Gopal initially had $150.
To determine how much money Gopal has left, we subtract the amount he spent from his initial amount:
Amount left = $150 - $110.
Amount left = $40.
So, Gopal has $40 left.