Question

a) Two numbers are in the ratio 4:5. When 6 is added to each term, their ratio becomes 5:6. Find the numbers.​

Answer 1

Step-by-step explanation:

Let x be the number.

Then,

Two numbers becomes 4x and 5x

Then,

6 is added to each term and their ratio becomes 5:6 -

4x + 6/ 5x + 6 = 5/6

(4x + 6)6 = (5x+6)5

24x + 36 = 25x + 30

x = 6

Then,

The numbers are -

1. 4x = 4×6 = 24
2. 5x = 5×6 = 30
3. 4x+6 = 4(6) + 6 = 30
4. 5x+6 = 5(6) + 6 = 36

Answer 2

$\\ \huge\mathfrak {\underline \purple{ \: \: \: \: \: \: \: \: question \mapsto \: \: \: \: \: \: \: \: }}$

➺ ᴛᴡᴏ ɴᴜᴍʙᴇʀs ᴀʀᴇ ɪɴ ᴛʜᴇ ʀᴀᴛɪᴏ 4:5 . ᴡʜᴇɴ 6 ɪs ᴀᴅᴅᴇᴅ ᴛᴏ ᴇᴀᴄʜ ᴛᴇʀᴍ , ᴛʜᴇɪʀ ʀᴀᴛɪᴏ ʙᴇᴄᴏᴍᴇs 5:6 . ғɪɴᴅ ᴛʜᴇ ɴᴜᴍʙᴇʀs.

$\\ \huge\mathfrak {\underline \purple{ \: \: \: \: \: \: \: \: solution \mapsto \: \: \: \: \: \: \: \: }}$

$\\ \large\sf \bold let \: the \: number \: be \: \red x \\ \\ \large\sf \bold so\: the \: number \: will \: be \: \red {4x \:} and \: \red{5x} \\ \\ \large\sf \bold adding \: \red6 \: to \: each \: term \\ \\ \large\sf \bold the \: numbers \: becomes\: \red {(4x + x) }\: and \: \red{(5x + x)} \\ \\ \large\sf \bold since \: the \:new \: ratio \: is \: \red{ 5 : 6 }\\ \\ \large \tt\blue➦ \frac{(4x + x)}{(5x + x)} = \frac{5}{6} \\ \\ \large\sf \bold by \:cross \: multiplying \\ \\ \large \tt\blue➦ 6(4x + x) = 5(5x + x) \\ \\ \large \tt\blue➦ 24x + 36 = 25x + 30 \\ \\ \large \tt\blue➦ 24x - 25x = 30 - 36 \\ \\ \large \tt\blue➦ \cancel- x = \cancel - 6$

$\\ \: \: \: \: \: \: \: \: \: \: \large\sf \bold therefore \: the \: numbers \: are \green\rightarrow \\ \\ \large \tt\blue ➲ \: 4x \: = \: 4 \times 6 \\ \: \: \: \: \: \: \large= 24 \\ \\ \large \tt\blue➲ \: 5x \: = \: 5 \times 6 \\ \: \: \: \: \: \: \large= 30$