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 $2x = 40$.