Question

Find the numbers.
11. Two numbers are in the ratio 3 : 5. If each number is increased by 10, the new numbers will be in the ratio 5: 7. Find the original numbers.
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Answer 1

GIVEN :-

• Ratio of two numbers = 3 : 5

• If each number is increased by 10 , the new numbers will be

       in the ratio 5 : 7 .

TO FIND :-

• Original numbers

SOLUTION :-

 Let ,

 One number = 3x

 Other number = 4x

  According to the question ,

         

      $\sf 3x+10:5x+10 = 5:7$

    $\longrightarrow \sf \dfrac{3x+10}{5x+10}=\dfrac{5}{7}\\\\\longrightarrow 7(3x+10)=5(5x+10)\\\\\longrightarrow 21x+70=25x+50 \\\\\longrightarrow 25x-21x=70-50\\\\\longrightarrow4x = 20 \\\\\longrightarrow\bf x=5$

The two original numbers are 15 and 25 .

Answer 2

Step-by-step explanation:

GIVEN :-

Ratio of two numbers = 3 : 5

If each number is increased by 10 , the new numbers will be

in the ratio 5 : 7 .

TO FIND :-

Original numbers

SOLUTION :-

Let ,

One number = 3x

Other number = 4x

According to the question ,

3x + 10 : 5x + 10 = 5:7

$\frac{3x + 10}{5 x + 10 } = \frac{5}{7}$

⟶7(3x+10)=5(5x+10)

⟶21x + 70=25x+50

⟶25x−21x=70−50

⟶4x=20

⟶x=5

The two original numbers are 15 and 25 .