Two numbers are respectively 35% and 80% more than... | JAMB UTME - Mathematics - 2023

Question 1 Report

Two numbers are respectively 35% and 80% more than a third number. The ratio of the two numbers is

7 : 16

3 : 4

16 : 7

4 : 3

Answer Details

Let's say the third number is x.

The first number is 35% more than x, so it is x + (35/100)x = x + (0.35)x = 1.35x.

The second number is 80% more than x, so it is x + (80/100)x = x + (0.8)x = 1.8x.

The ratio of the two numbers is (first number)/(second number) = (1.35x)/(1.8x) = 1.35/1.8 = 0.75.

Now, to simplify the ratio, we multiply both the numerator and denominator by 4 to get:

(1.35/1.8) * 4 = (1.35*4)/(1.8*4) = 5.4/7.2.

The simplified ratio is 5.4 : 7.2.

This ratio can be further simplified by dividing both numbers by their greatest common divisor, which is 1.8.

So, dividing both numbers by 1.8, we get 3 : 4.

Therefore, the ratio of the two numbers is 3 : 4.

Two numbers are respectively 35% and 80% more than a third number. The ratio of the two numbers is