Question

Two no are in ratio 2:5 if 16 is added to both the no the ratio will become 1:2 what are the no

Answer 1

Let the numbers are 2x and 5x respectively.

∴ If 16 will be added to the numbers, new numbers will be,

2x + 16 and 5x + 16

According to the Question,

(2x + 16)/(5x + 16) = 1/2

⇒ 2(2x + 16) = 5x + 16

⇒ 4x + 32 = 5x + 16

∴ 5x - 4x = 32 - 16

∴ x = 16

Now, numbers will be,

2x = 2 × 16 = 32

5x = 5 × 16 = 80

Hope it helps.

Answer 2

Let the two numbers be x and y.

Given:

x:y = 2:5

x/y = 2/5

5x -2y =0......(1)

When 16 is added to these numbers,

(x+16)/ (y+16) = 1/2

2x + 32 = y+16

2x+ 16 = y.....(2)

using (2) in (1)

5x - 2(2x +16) =0

==> x = 32

(2)==> y = 80.

I hope this answer helps you