Answer:
The amount with r is rs. 2400.
Explanation:
Let's denote the amount of money with:
p as the amount with person P,
q as the amount with person Q, and
r as the amount with person R.
We are given that the three individuals have a total of Rs. 6000 among themselves, so we can write the equation:
p + q + r = 6000
We are also given that person R has two-thirds of the total amount with persons P and Q. So, we can express this as:
r = (2/3)(p + q)
Now we can substitute this expression for r into the first equation:
p + q + (2/3)(p + q) = 6000
To solve for r, we need to simplify and solve for p and q first. Let's do that:
Multiplying the entire equation by 3 to eliminate the fraction:
3p + 3q + 2p + 2q = 18000
Combine like terms:
5p + 5q = 18000
Now, divide both sides by 5 to solve for p + q:
p + q = 18000 / 5
p + q = 3600
Now that we know p + q is 3600, we can substitute this value back into the equation for r:
r = (2/3)(3600)
r = 2400
So, the amount with person R is Rs. 2400.