The sum of two natural numbers is 240 and their ratio is 3 : 5. Then the greater number is

1. 180

2. 160

3. 150

4. 90

Let the two numbers be x and y.

Given, sum = 240.

∴ x + y = 240

⇒ x = 240 - y ……..(i)

$\therefore \dfrac{x}{y} = \dfrac{3}{5}$ ……(ii)

Substituting value of x from (i) in (ii) we get,

$\Rightarrow \dfrac{240 - y}{y} = \dfrac{3}{5} \\[1em] \Rightarrow 5(240 - y) = 3y \\[1em] \Rightarrow 1200 - 5y = 3y \\[1em] \Rightarrow 8y = 1200 \\[1em] \Rightarrow y = 150.$

Substituting value of y in (i) we get,

⇒ x = 240 - 150 = 90.

Hence, Option 3 is the correct option.