Divide Rs. 3000 into three parts in such a way that one third of the first part, one fifth of the second part, and one seventh of the third part are equal.

To divide Rs. 3000 into three parts in such a way that one-third of the 1st part, one-fifth of the 2nd part, and one-seventh of the 3rd part are equal, we can use algebraic equations to solve for the values of the parts. The three parts are Rs. 9000, Rs. 15000, and Rs. 21000.

Explanation:

To divide Rs. 3000 into three parts such that one-third of the first part, one-fifth of the second part, and one-seventh of the third part are equal, we can use algebraic equations.

Let's assume the three parts are a, b, and c.
According to the given conditions,
- a/3 = b/5
- b/5 = c/7
We can simplify these equations as follows:
- 5a = 3b
- 7b = 5c
From the first equation, we can find a relationship between a and b:

b = (5/3)a

Substituting this value of b in the second equation, we get:

7(5/3)a = 5c

Simplifying, we find:

c = (7/5)(5/3)a

Since we know that a + b + c = Rs. 3000, we can substitute the values of b and c in terms of a into this equation and solve for a:

a + (5/3)a + (7/5)(5/3)a = 3000
15a + 25a + 35a = 3000 * 225
75a = 3000 * 225
a = (3000 * 225) / 75
a = Rs. 9000

Substituting the value of a back into the equations, we can find the values of b and c:

b = (5/3)(9000) = Rs. 15000
c = (7/5)(5/3)(9000) = Rs. 21000

Learn more about Algebraic Equations here:

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