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, \(a = 10 \times 4 = 40\).
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 $2x = 40$.
List-I (Words) | List-II (Definitions) |
(A) Theocracy | (I) One who keeps drugs for sale and puts up prescriptions |
(B) Megalomania | (II) One who collects and studies objects or artistic works from the distant past |
(C) Apothecary | (III) A government by divine guidance or religious leaders |
(D) Antiquarian | (IV) A morbid delusion of one’s power, importance or godliness |