A and B together have Rs 1,500. If `1//4^(th)` of A's amount is equal to `2//4^(th)` of B's, then how much amount A has ?

Options

A. Rs 2,000
B. Rs 5,000
C. Rs 1,500
D. Rs 1,000

Answer

To solve the problem step by step, let's denote the amounts that A and B have as follows:

Let:
- A's amount = x
- B's amount = y

According to the problem, we have two key pieces of information:

1. A and B together have Rs 1,500:
\[ x + y = 1500 \quad \text{(Equation 1)} \]

2. One-fourth of A's amount is equal to two-fourths of B's amount:
\[ \frac{1}{4}x = \frac{2}{4}y \]
Simplifying the second equation gives:
\[ \frac{1}{4}x = \frac{1}{2}y \]
To eliminate the fractions, we can multiply both sides by 4:
\[ x = 2y \quad \text{(Equation 2)} \]

Now, we can substitute Equation 2 into Equation 1:

Substituting \(x = 2y\) into \(x + y = 1500\):
\[ 2y + y = 1500 \]
This simplifies to:
\[ 3y = 1500 \]

Now, we can solve for y:
\[ y = \frac{1500}{3} = 500 \]

Now that we have the value of y, we can find the value of x using Equation 2:
\[ x = 2y = 2 \times 500 = 1000 \]

Thus, the amount that A has is:
\[ \text{A's amount (x)} = 1000 \]

### Final Answer:
A has Rs 1000.