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.