A's money is to B's money as 4:5 and B's money is to C's money as 2:3 if A has Rs.800 C has

Options

A. Rs.1000
B. Rs.1200
C. Rs.1500
D. Rs.2000

Answer

To solve the problem step by step, we will use the ratios provided and the information about A's money to find out how much C has.

### Step 1: Understand the Ratios
We are given two ratios:
1. A's money to B's money is 4:5.
2. B's money to C's money is 2:3.

### Step 2: Express A, B, and C in Terms of a Common Variable
Let’s denote:
- A's money = 4x (where x is a common multiplier)
- B's money = 5x (from the first ratio)

From the second ratio (B's money to C's money), we can express C's money in terms of B:
- B's money = 2y (where y is another common multiplier)
- C's money = 3y

### Step 3: Equate B's Money from Both Ratios
Since B's money is expressed in two different ways, we can set them equal to each other:
5x = 2y

### Step 4: Solve for y in Terms of x
From the equation 5x = 2y, we can solve for y:
y = (5/2)x

### Step 5: Substitute y to Find C's Money
Now substitute y into the expression for C's money:
C's money = 3y = 3 * (5/2)x = (15/2)x

### Step 6: Use the Given Value of A to Find x
We know that A's money is Rs. 800:
4x = 800
=> x = 800 / 4 = 200

### Step 7: Calculate C's Money
Now substitute x back into the expression for C's money:
C's money = (15/2)x = (15/2) * 200 = 15 * 100 = 1500

### Final Answer
C has Rs. 1500.

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