Correct Answer - Option 2 : 14

Given:

After subtracting 5 from the greatest number and 7 from the smallest number, then the ratio is 3 ∶ 1

Also, the sum of the numbers is 24

Concept Used:

A ratio indicates how many times one number contains another.

Calculation:

Let the numbers be x and y respectively

∴ x + y = 24 ----(1)

Also, when subtraction of 5 from the greatest number and subtraction of 7 from the smallest number, then the ratio is 3 ∶ 1

So, \({x - 5 \ \over y - 7} ={3 \ \over 1}\)

⇒ 1 × (x - 5) = 3 × (y - 7)

⇒ x - 5 = 3y - 21

⇒ x - 3y = -16 (2)

Solving equation (1) and (2), we get

x = 14 and y = 10

The greater number = 14

∴ The greater number is 14.