Question

The difference between two whole numbers is 66.the ratio of two numbers is 2:5.what are the two numbers

Answer 1

Step-by-step explanation:

Let the two numbers be x and y respectively.

Given,

$\frac{x}{y} = \frac{2}{5} \\ x = \frac{2y}{5}$

Now considering difference, since we don't know which is greater number, we will consider modulus of their difference.

So,

$|y - x| = 66 \\ | y - \frac{2y}{5} | = 66 \\ \frac{3y}{5} = 66 \\ \frac{y}{5} = 22 \\ y = 110$

Now by the relation given in the question,

$x = \frac{2y}{5} = \frac{2 \times 110}{5} = \frac{220}{5} = 44$

So, the two numbers are 44 and 110.

Thank you

Answer 2

Answer:

110 &44

Step-by-step explanation:

The numbers: a&b

The difference: a-b=66 => a=b+66

The ratio: b/a=2/5 => a=5b/2

b+66=5b/2 =>2b+132=5b =>3b=132 =>b= 132/3=44

b=44

a=b+66=44+66=110