Two numbers are respectively 46% and 54% more than a third number. The ratio of the two numbers is:

Correct option is A

Given:

Two numbers are respectively 46% and 54% more than a third number.

Concept Used:

If a number is ‘a% more’ than another number x, then it is given by:

= x × (1 + a/100)

The ratio of two numbers a and b is given by a : b and can be simplified using HCF.

Solution:

Let the third number be x.

Then, First number = x × (1 + 46/100) = 1.46x

Second number = x × (1 + 54/100) = 1.54x

Required Ratio = 1.46x : 1.54x = 1.46 : 1.54

To simplify, multiply both terms by 100: 146 : 154

Now, find HCF of 146 and 154, which is 2.

=> Simplified Ratio = 146 ÷ 2 : 154 ÷ 2 = 73 : 77

73 : 77