Question

The ratio of numerator and denominator of the rational number is 2:7 and if 4 is added to the numerator and 2 is subtracted from the denominator the rational number becomes 10/19. find the original number​.

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Answer 1

Given:

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• The ratio of numerator and denominator of the rational number is 2:7.

• If 4 is added to the numerator and 2 is subtracted from the denominator the rational number becomes 10/19.

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To find:

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• Original number?

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Solution:

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☯ Let Numerator and Denominator of rational no. be 2x and 7x respectively.

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$\underline{\bigstar\:\boldsymbol{According\:to\:the\:question\::}}$

• If 4 is added to the numerator and 2 is subtracted from the denominator the rational number becomes 10/19.

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$:\implies\sf \dfrac{2x + 4}{7x - 2} = \dfrac{10}{19}$

$:\implies\sf 19(2x + 4) = 10(7x - 2)$

$:\implies\sf 38x + 76 = 70x - 20$

$:\implies\sf 38x - 70x = - 20 - 76$

$:\implies\sf - 32x = - 96$

$:\implies\sf x = \cancel{ \dfrac{96}{32}}$

$:\implies{\boxed{\sf{\purple{x = 3}}}}\;\bigstar$

Therefore,

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• Numerator of required rational no., 2x = 2 × 3 = 6
• Denominator of required rational no., 5x = 7 × 3 = 21

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$\therefore$ Hence, The original number is 6/21.

Answer 2

Given :

• The ratio of numerator and denominator of the rational number is 2:7

• if 4 is added to the numerator and 2 is subtracted .

• the denominator the rational number becomes 10/19.

To Find :

• find the original number.

Solution :

• Let the numerator be x

• Let the denominator be y

According to the Question :

• The ratio of numerator and denominator of the rational number is 2:7

x/y = 2/7

7x = 2y

• 7x - 2y = 0 ........ ( 1 )

According to the Question :

• if 4 is added to the numerator and 2 is subtracted from the denominator the rational number becomes 10/19.

x + 4/y - 2 = 10/19

19x + 76 = 10y - 20

19x - 10y = - 20 - 76

• 19x - 10y = - 96 ........ ( 2 )

By eliminating method

• 10 multiplying in equ 1 and 2 multiplying. in equ 2

70x - 20y = 0

38x - 20y = - 192

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32x = 192

x = 192 / 32

x = 6

Substitute the value of x in equ 1

7 × 6 - 2y = 0

42 - 2y = 0

- 2y = - 42

y = 42/2

y = 21

• Hence the original number is 6/21