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

Let the three numbers be \(a\), \(b\), and \(c\). We are given that \(a + b + c = 136\). We are also given that \(a:b = 2:3\) and \(b:c = 5:3\).

To find a common ratio for all three numbers, we need to make the \(b\) values in both ratios the same. The LCM of 3 and 5 is 15. So we multiply the first ratio by 5 to get \(a:b = 10:15\) and the second ratio by 3 to get \(b:c = 15:9\).

Now we have a combined ratio of \(a:b:c = 10:15:9\).

This means \(a = 10x\), \(b = 15x\), and \(c = 9x\) for some value \(x\). Substituting into the equation \(a + b + c = 136\), we get:

\(10x + 15x + 9x = 136\)

\(34x = 136\)

\(x = \frac{136}{34} = 4\)

Therefore, \(a = 10 \times 4 = 40\).

Answer 2

Let the numbers be $2x$, $3x$, and $\frac{9x}{5}$. 

Their sum is 136: $2x + 3x + \frac{9x}{5} = 136 \Rightarrow 34x = 680 \Rightarrow x = 20$. 

The first number is $2x = 40$.