Question

Two numbers are in the ratio 2 : 5. If 16 is added to both the numbers, their ratio becomes 1 : 2. The numbers are :

Answer 1

Two numbers are in the ratio 2 : 5

Let the constant be x

So, let the 1st number be 2x and 2nd number be 5x

After adding 16 to each, 1st number = 2x + 16 and 2nd number = 5x + 16

After adding 16 to each, the ratio of the numbers becomes 1 : 2


According to the question,

$\dfrac{2x + 16}{5x + 16} = \dfrac{1}{2}$

➾ 2(2x + 16) = 1(5x + 16)

➾ 4x + 32 = 5x + 16

➾ 4x - 5x = 16 - 32

➾ -x = -16

By cancelling the minus (-) signs,

➾ x = 16



∴ 1st number ➾ 2x

➾ 2 × 16

➾ $\red{\boxed{\boxed{\boxed{\green{32}}}}}$



∴ 2nd number ➾ 5x

➾ 5 × 16

➾ $\red{\boxed{\boxed{\boxed{\green{80}}}}}$

Answer 2

$\underline\bold{Step-by-step \: explanation}$

The ratios can be 2x/5x

As 16 is added to them so,

$\frac{2x+16}{5x+16}= [tex]\frac{1}{2}$

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

x= 5x+16= 4x+ 32

x= 16

The numbers before adding 16 were,

2x= 2×16= 32

5x= 5×16= 80

The numbers were 32:80.

The ratio before adding 16 was $\boxed{32:80}$
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Hope it helps u