Question

The sum of three numbers is 136. If the ratio between the first number and the second number is 2:3, and that between the second and the third number is 5:3, then the first number is:

• A. 42
• B. 40
• C. 36
• D. 32

Answer 1

The Correct Option is B

To determine the first number, we must establish the relationship between three numbers given their ratios and their total sum. Let the numbers be denoted by \(x\), \(y\), and \(z\), where \(x\) is the first number we aim to find.

1. Given the total sum:

\(x + y + z = 136\)

The ratio of the first to the second number is 2:3, which can be expressed as:

\( \frac{x}{y} = \frac{2}{3} \Rightarrow x = \frac{2}{3}y\)

1. The ratio of the second to the third number is 5:3, yielding:

\(\frac{y}{z} = \frac{5}{3} \Rightarrow z = \frac{3}{5}y\)

1. Substitute the expressions for \(x\) and \(z\) into the sum equation:

\(\frac{2}{3}y + y + \frac{3}{5}y = 136\)

1. Simplify and solve for \(y\):

\(\frac{2}{3}y + y + \frac{3}{5}y = 136\)

Find a common denominator (15) to combine the terms:

\(\frac{10}{15}y + \frac{15}{15}y + \frac{9}{15}y = 136\)

\(\frac{10y + 15y + 9y}{15} = 136\)

\(\frac{34y}{15} = 136\)

Multiply both sides by 15:

\(34y = 136 \times 15\)

\(34y = 2040\)

Solve for \(y\):

\(y = \frac{2040}{34}\)

\(y = 60\)

1. Substitute the value of \(y\) back into the equation for \(x\):

\(x = \frac{2}{3}y = \frac{2}{3} \times 60 = 40\)

Therefore, the first number is 40.