Question

If the ratio between the first number and the second number is 2:3 and that between the second and third number is 5:3, then the first number is:

• A. 6
• B. 12
• C. 15
• D. 18

Answer 1

The Correct Option is A

The problem is solved using the provided ratio information. The numbers are defined as follows:

1. The ratio of the first to the second number is \(2:3\). Let the first number be \(2x\) and the second number be \(3x\).
2. The ratio of the second to the third number is \(5:3\). Using \(3x\) for the second number, let the third number be \(3y\). This gives the equation \(\frac{3x}{3y}=\frac{5}{3}\).
3. Solve for \(x\) in terms of \(y\) from the equation \(\frac{3x}{3y}=\frac{5}{3}\):

\[3x=5 \cdot 3y\]

\[3x=15y\]

\[x=5y\]

1. Substitute \(x=5y\) into the expression for the first number, \(2x\):

\[2x=2 \cdot 5y=10y\]

1. Given that \(10y\) represents the first number, compare it with the provided options. Assuming the answer is 6, then \(10y=6\):

\[10y=6\]

\[y=\frac{6}{10}=0.6\]

Substitute the value of \(y\) back to find \(x\):

\[x=5 \cdot 0.6=3\]

1. The first number is calculated as \(2x=2 \cdot 3=6\).