Math, asked by bhanushalipremila212, 5 months ago

Two number are in the ratio 5:4.If 5bis added to the greater number and 5 is. subtracted from the smaller one,then their ratio of 2:1.find the number

Answers

Answered by prabhas24480
1

Let the numbers be x and 3x 

Then, 

          3x+5x+5=21

          ⇒2x+10=3x+5

          ⇒x=5 

Hence, the numbers are 5 and 15 

∴ Sum of numbers = 20

Answered by Anonymous
9

\huge{ \green{ \underline{ \mathfrak{Given:}}}}

  • Ratio of two numbers = 5:4
  • Ratio (After adding and subtracting 5) = 2:1

\huge{ \green{ \underline{ \mathfrak{To  \: Find : }}}}

  • The numbers

\huge{ \green{ \underline{ \mathfrak{Solution:}}}}

Put x in the ratio,

  • First number = 5x (Greater number)
  • Second number = 4x (Smaller number)
  • First number (After adding 5) = 5x + 5
  • Second number (After subtracting 5) = 4x 5

According to question,

 \large{ \sf :  \implies \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \frac{5x + 5}{4x - 5}  =  \frac{2}{1} } \\

After cross multiplication,

 \large{ \sf :  \implies \:  \:  \:  \:  \:  \:  \:  \:  \:  \: 1(5x + 5) = 2(4x - 5)}

 \large{ \sf :  \implies \:  \:  \:  \:  \:  \:  \:  \:  \:  \: 5x + 5 = 8x - 10}

 \large{ \sf :  \implies \:  \:  \:  \:  \:  \:  \:  \:  \:  \: 5x - 8x =  - 10 - 5}

 \large{ \sf :  \implies \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  - 3x =  - 15}

 \large{ \sf :  \implies \:  \:  \:  \:  \:  \:  \:  \:  \:  \: x = 5}

Now:

  • First number = 5x = 25
  • Second number = 4x = 20

\huge{ \green{ \underline{ \mathfrak{ Hence: }}}}

  • The numbers are 25 and 20 respectively
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