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

To solve the problem, we'll use the given information about the ratios between the numbers. Let's define the numbers:

1. The ratio between the first number and the second number is \(2:3\). Assume the first number is \(2x\) and the second number is \(3x\).
2. The ratio between the second number and the third number is \(5:3\). Use \(3x\) for the second number and assume the third number is \(3y\), so we have ​\(\frac{3x}{3y}=\frac{5}{3}\).
3. From \(\frac{3x}{3y}=\frac{5}{3}\), solve for \(x\) in terms of \(y\):

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

\[3x=15y\]

\[x=5y\]

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

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

1. Given that \(10y\) is the expression for the first number, match against the options provided. According to the answer given (6), \(10y=6\):

\[10y=6\]

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

Substitute \(y\) back to find \(x\):

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

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