Question

The sum of 2 numbers is 68 and the
difference between them is 4.
Their ratio is
(A) 9:8
(B)
6:4
(C) 3:2
(D) 2:3​

Answer 1

$\Large{\bf{\green{\mathfrak{\dag{\underline{\underline{Given:-}}}}}}}$

• The sum of 2 numbers is 68 and the
• difference between them is 4.

$\Large{\bf{\orange{\mathfrak{\dag{\underline{\underline{To \: Find:-}}}}}}}$

• The ratio of the numbers

$\Large{\bf{\red{\mathfrak{\dag{\underline{\underline{Solution:-}}}}}}}$

• Let the 2 numbers be x and y.

According to the question,

• The sum of 2 numbers is 68.

Therefore,

• x + y = 68 $\longrightarrow \boxed{1}$

According to the question,

• The difference between the numbers is 4.

Therefore,

• x - y = 4

• x = 4 + y

Substituting x = 4 + y in $\boxed{1}$ ,

• x + y = 68

• 4 + y + y = 68

• 4 + 2y = 68

• 2y = 68 - 4

• 2y = 64

• $\sf y \: = \: \dfrac{64}{2}$

• $\sf y \: = \: \dfrac{\cancel{64}}{\cancel{2}}$

Therefore,

• $\underline{\bf{\pink{\sf y \: = \: 32}}}$

Substituting y = 32 in $\boxed{1}$ ,

• x + y = 68

• x + 32 = 68

• x = 68 - 32

Therefore,

• $\underline{\bf{\pink{\sf x \: = \: 36}}}$

Now,

• Ratio of the numbers,

• x : y

• 36 : 32

Dividing by 4,

• 9 : 8

Therefore,

• $\underline{\boxed{\therefore{\blue{\sf Ratio \: between \: the \: numbers \: = \: 9 \: : \: 8.}}}}$

• $\underline{\boxed{\therefore{\blue{\sf The \: correct \: option \: is \: (A) \: 9 \: : \: 8.}}}}$

Answer 2

${\large{\pmb{\sf{\underline{RequirEd \; Solution...}}}}}$

${\bigstar \:{\underline{\underline{\pmb{\sf{\purple{Understanding \: the \: Question:}}}}}}}$

⋆ This question says that the sum of 2 numbers is 68 and the difference between them is 4. We have to find out the ratio between them. Some options are given for help, these options are 9:8, 6:4, 3:2 and 2:3 Let us solve this question!

${\bigstar \:{\underline{\underline{\pmb{\sf{\purple{Given \: that:}}}}}}}$

⋆ There are two numbers.

⋆ The sum of these two numbers = 68

⋆ Difference between these numbers = 4

${\bigstar \:{\underline{\underline{\pmb{\sf{\purple{To \: find:}}}}}}}$

⋆ The ratio between these numbers

${\bigstar \:{\underline{\underline{\pmb{\sf{\purple{Solution:}}}}}}}$

⋆ The ratio between these numbers = 9:8

${\bigstar \:{\underline{\underline{\pmb{\sf{\purple{Full \: Solution:}}}}}}}$

~ As it's given that the sum of the two given numbers is 68. Henceforth, according to the statement let

• ${\sf{a \: is \: first \: number}}$
• ${\sf{b \: is \: second \: number}}$

~ Henceforth, as it's given that 68 is their sum. So, it became

${\sf{:\implies a \: is \: first \: number}}$

${\sf{:\implies b \: is \: second \: number}}$

${\sf{:\implies a + b = 68}}$

~ It is also given that their difference between these numbers are 4. So according to the statement:

${\sf{:\implies a \: is \: first \: number}}$

${\sf{:\implies b \: is \: second \: number}}$

${\sf{:\implies a - b = 4}}$

${\sf{:\implies a = 4+b}}$

${\underline{\sf{Henceforth, \: value \: of \: a \: is \: 4+b}}}$

~ Now again as it's given that 68 is their sum. So now it became

${\sf{:\implies a \: is \: first \: number}}$

${\sf{:\implies b \: is \: second \: number}}$

${\sf{:\implies a + b = 68}}$

${\sf{:\implies 4+b+b = 68}}$

${\sf{:\implies 4+2b = 68}}$

${\sf{:\implies 2b = 68-4}}$

${\sf{:\implies 2b = 64}}$

${\sf{:\implies b = 64/2}}$

${\sf{:\implies b = 32}}$

${\underline{\sf{Henceforth, \: value \: of \: b \: is \: 32}}}$

~ Now let's find the perfect value of a by using the value of b.

${\sf{:\implies a \: is \: first \: number}}$

${\sf{:\implies b \: is \: second \: number}}$

${\sf{:\implies a + 32 = 68}}$

${\sf{:\implies a = 68-32}}$

${\sf{:\implies a = 36}}$

${\underline{\sf{Henceforth, \: value \: of \: a \: is \: 36}}}$

~ Now as it's given that we have to find out the ratio. Henceforth,

${\sf{:\implies Ratio \: = a:b}}$

${\sf{:\implies Ratio \: = 36:32}}$

${\sf{:\implies Ratio \: = \dfrac{36}{32}}}$

${\sf{:\implies Ratio \: = \cancel{\dfrac{36}{32}}}}$

${\sf{:\implies Ratio \: = \cancel{\dfrac{18}{16}}}}$

${\sf{:\implies Ratio \: = \dfrac{9}{8}}}$

${\sf{:\implies Ratio \: = 9:8}}$

${\underline{\sf{Henceforth, \: ratio \: between \: them \: is \: 9:8}}}$