Question

Two numbers are in the ratio 3:5. If 10 is subtracted from each of them then the ratio becomes 1:5. Find the greater number.​

Answer 1

Given:-

• Ratio of two numbers is 3:5.
• 10 is subtracted from each of them, then ratio becomes 1:5.

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To find:-

• The greater number among them.

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Solution:-

Let,

• the two numbers be 3x and 5x, the greater number among them is 5x.

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According to the question,

→ (3x - 10)/(5x - 10) = 1:5

→ (3x - 10)/(5x - 10) = 1/5

→ 5(3x - 10) = 1(5x - 10)

→ 15x - 50 = 5x - 10

→ 15x - 5x = - 10 + 50

→ 10x = 40

→ x = 40/10

→ x = 4

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Hence,

• Greater number = 5x = 5(4) = 20
• Other number = 3x = 3(40) = 12

Answer 2

Given :-

• Ration of the number is 3 : 5.
• 10 is subtracted from each of them , then ration becomes 1 : 5.

To find :-

• The greater number among them.

Solution :-

Let's do it,

• The two numbers be 3x and 5x , the greater number among them is 5x.

$~~~~~~~~~~~~$ According to the question,

:$\implies$ $\large{\tt{\frac{(3x - 10)}{5x - 10} = 1 : 5}}$

:$\implies$ $\large{\tt{\frac{(3x - 10)}{(5x - 10)} = \frac{1}{5}}}$

:$\implies$ $\large{\tt{5(3x - 10) = 1(5x - 10)}}$

:$\implies$ $\large{\tt{15x - 50 = 5x - 10}}$

:$\implies$ $\large{\tt{15x - 5x = -10 + 50}}$

:$\implies$ $\large{\tt{10x = 40}}$

:$\implies$ $\large{\tt{x = \frac{40}{10} }}$

:$\implies$ $\large{\tt{x = 4}}$

Hence,

• Greater number 5x = 5(4) = 20
• Other number 3x = 3(40) = 12.