Divide Rs 116 among 4 parts such that 5 added to first part 4 subtracted from the second part 3 mutltiplied by third part and fourth part divided by 2 are all equal
a+b+c+d = 116
a+5 = b-4 = 3c = d/2
22,31,9,54
To solve this problem, we'll start by assuming the amount of money in each part is x, so we have 4 equal parts: x + x + x + x = 4x.
According to the given conditions:
- If we add 5 to the first part, it will be x + 5.
- If we subtract 4 from the second part, it will be x - 4.
- If we multiply the third part by 3, it will be 3x.
- If we divide the fourth part by 2, it will be x/2.
According to the problem, these four expressions are equal to each other. So we can equate them:
x + 5 = x - 4 = 3x = x/2
Now we'll solve this equation step by step:
1. x + 5 = x - 4
Subtracting x from both sides, we get:
5 = -4
This is not possible, so this equation is not valid.
2. x + 5 = 3x
Subtracting x from both sides, we get:
5 = 2x
Dividing both sides by 2, we get:
2.5 = x
We have found the value of x, which is 2.5.
Now, let's check if the fourth condition is also satisfied:
x/2 = 2.5/2 = 1.25
Since all the conditions are satisfied, we can conclude that the total amount of Rs 116 can be divided into four parts such that adding 5 to the first part, subtracting 4 from the second part, multiplying the third part by 3, and dividing the fourth part by 2 all result in the same value.
To find the actual amount for each part, we multiply 2.5 by 4:
2.5 * 4 = 10
Therefore, the four parts will be Rs 10, Rs 10, Rs 10, and Rs 10.