Question

8. Two numbers are in the ratio 4: 5. If 5 is added to each number, the ratio becomes 13:16. Find the numbers.​

Answer 1

${\huge{\orange{\:\:\:\:\:\:\:\:\:Ꮧռʂաɛʀ\:\:\:\:\:\:\:\:}}}$

Let the numbers be 4x and 5x.

So,the ratio = 4x : 5x

Now, it becomes

⇒4x + 5 : 5x + 5 = 13:16

⇒4x+5/5x+5=13/16

⇒65x + 65 = 64x + 80 {Doing Cross-Multiplication}

⇒65x - 64x = 80-65 {transposing numbers}

⇒x=15

So , the numbers are ,

4x = 4*15 = 60

5x = 5*15=75

Answer 2

Let the numbers be 4x and 5x

If 5added to them then the numbers are

• 4x+5
• 5x+5

ATQ

$\\ \sf \longmapsto \: \frac{4x + 5}{5x + 5} = \frac{13}{16} \\ \\ \sf \longmapsto \: 16(4x + 5) = 13(5x + 5) \\ \\ \sf \longmapsto \: 64x + 80 = 65x + 65 \\ \\ \sf \longmapsto \: 64x - 65x = 65 - 80 \\ \\ \sf \longmapsto \: - x = - 15 \\ \\ \sf \longmapsto \: x = 15 \\ \bull \bf \: the \: numbers \: are \\ \\ \sf \longmapsto \: 4x = 4(15) = 60 \\ \\ \sf \longmapsto \: 5x = 5(15) = 75$