Question

There are two numbers in the ratio 7:5. If 2 is subtracted from each of them,the ratio becomes 3:2. Find the numbers​

Answer 1

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Answer 2

Given

• Ratio of two numbers is 7:5.
• If 2 is subtracted from each of them, the ratio becomes 3:2.

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To find

• The numbers.

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Solution

• Let the ratio of given numbers be x. Then,

→ First number = 7x

→ Second number = 5x

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• As given in the question, if 2 is subtracted from both numbers, then the ratio becomes 3:2.

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$\tt:\implies\: \: \: \: \: \: \: \: {\dfrac{7x - 2}{5x - 2} = \dfrac{3}{2}}$

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$\tt:\implies\: \: \: \: \: \: \: \: {2(7x - 2) = 3(5x - 2)}$

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$\tt:\implies\: \: \: \: \: \: \: \: {14x - 4 = 15x - 6}$

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$\tt:\implies\: \: \: \: \: \: \: \: {15x - 14x = 6 - 4}$

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$\tt:\implies\: \: \: \: \: \: \: \: {x = 2}$

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• By putting the values

→ First number = 7x = 14

→ Second number = 5x = 10

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Hence,

• The required numbers are 14 and 10.