Two numbers are in the ratio 7:4. If their difference is 72, find the numbers
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2 thoughts on “<br />Two numbers are in the ratio 7:4. If their difference is 72, find the numbers<br />​”

1. Answer :

   • The numbers are 168 and 96

   Given :

   • Two numbers are in the ratio is 7:4
   • Difference is 72

   To find :

   • The numbers

   Solution :

   • Let the first number be 7x
   • Let the second number be 4x

   Given that, the difference is 72 so,

   According to Question,

   》7x – 4x = 72

   》3x = 72

   》x = 72/3

   》x = 24

   Then,

   • First number = 7x = 7(24) = 168
   • Second number = 4x = 4(24) = 96

   Hence, The numbers are 168 and 96

   Verification :

   》7x – 4x = 72

   》7(24) – 4(24) = 72

   》168 – 96 = 72

   》72 = 72

   Hence verified

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2. [tex] \mathfrak {Given}\begin{cases} \sf \: Two \: numbers \: are \: in \: the \: ratio \: \bold{7 : 4}. \\ \\ \sf Difference \: of \: those \: numbers \: is \: \bold{72}.\end{cases}[/tex]

   Need to find : Those numbers.

   ⠀⠀⠀⠀⠀⠀____________________

   Let the numbers be 7k and 4k respectively.

   [tex] \: \: [/tex]

   It is given that their difference is 72.

   [tex] \: \: [/tex]

   [tex] \mathfrak{ \underline{ \bigstar \: substituting \: the \: values \: : }}[/tex]

   [tex] \: [/tex]

   [tex] \sf : \implies \: 7k – 4k = 72 \\ \\ \\ \sf : \implies3k = 72 \\ \\ \\ \sf : \implies \: k = \cancel\frac{72}{3} \\ \\ \\ \: \sf : \implies \underline{\boxed{\mathfrak\pink{k = 24}}} \: \bigstar[/tex]

   [tex] \: \: [/tex]

   Now, put the value of k in the ratio.

   [tex] \: \: [/tex]

   • First number = 7k = 7(24) = 168
   • Second number = 4k = 4(24) = 96

   ⠀⠀⠀⠀⠀⠀____________________

   [tex]\sf\therefore{\underline{Hence, \: the \: two \: numbers \: are \: \bold{168} \: and \: \bold{96} \: respectively.}}[/tex]

   [tex] \: \: [/tex]

   [tex] \mathfrak {\underline{ \bigstar \: Verification \: :}}[/tex]

   [tex] \: \: [/tex]

   [tex] \sf : \implies \: 7k – 4k = 72 \\ \\ \\ \sf : \implies \: 3k = 72 \\ \\ \\ \sf : \implies3(24) = 72 \\ \\ \\ \sf : \implies72 = 72[/tex]

   [tex] \: \: [/tex]

   ⠀⠀⠀⠀⠀⠀____________________

   [tex]\sf\therefore{\underline{Hence, \: verified \: \: }}[/tex]

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