Out of two numbers, 40% of the greater number is equal to 60% of the smaller. If the sum of the numbers is 150, then the greater number is

Options

A. 70
B. 80
C. 90
D. 60

Answer

To solve the problem step by step, let's denote the greater number as \( x \) and the smaller number as \( y \).

### Step 1: Set up the equation based on the given information
We know that 40% of the greater number is equal to 60% of the smaller number. This can be expressed mathematically as:
\[ 0.4x = 0.6y \]

### Step 2: Simplify the equation
To eliminate the decimals, we can multiply both sides of the equation by 10:
\[ 4x = 6y \]
Now, we can simplify this equation by dividing both sides by 2:
\[ 2x = 3y \]

### Step 3: Express one variable in terms of the other
From the equation \( 2x = 3y \), we can express \( x \) in terms of \( y \):
\[ x = \frac{3}{2}y \]

### Step 4: Use the sum of the numbers
We are also given that the sum of the two numbers is 150:
\[ x + y = 150 \]

### Step 5: Substitute for \( x \)
Now, substitute \( x \) from the previous equation into the sum equation:
\[ \frac{3}{2}y + y = 150 \]

### Step 6: Combine like terms
To combine the terms on the left side, we can express \( y \) as \( \frac{2}{2}y \):
\[ \frac{3}{2}y + \frac{2}{2}y = 150 \]
\[ \frac{5}{2}y = 150 \]

### Step 7: Solve for \( y \)
Now, multiply both sides by 2 to eliminate the fraction:
\[ 5y = 300 \]
Now, divide both sides by 5:
\[ y = 60 \]

### Step 8: Find \( x \)
Now that we have \( y \), we can find \( x \) using the equation \( x = \frac{3}{2}y \):
\[ x = \frac{3}{2} \times 60 = 90 \]

### Conclusion
Thus, the greater number is:
\[ \boxed{90} \]