Question

Two number are such that the ratio between them is 3:5 .If each is increased by10 ,the ratio between the new number be formed is 5 :7.Find the original numbers

Answer 1

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GIVEN :

=> THE RATIO OF 2 NO. :

=> 3 : 5

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LET,

=> X BE THE COMMON MULTIPLE OF THIS RATIO

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FIRST NO. :

=> 3 * X

=> 3X

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SECOND NO.

=> 5 * X

=> 5X

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CONDITION ,

=> IF EACH ONE IS INCREASED BY 10 :

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NEW FIRST NO.

=> 3X + 10

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NEW SECOND NO.

=> 5X + 10

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THE RATIO OF NEW NO.

=> 5 : 7

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

=> 7 ( 3X + 10 ) = 5 ( 5X + 10 )

=> 21X + 70 = 25X + 50

=> 70 - 50 = 25X - 21X

=> 20 = 4X

=> X = 20 / 4

$\huge\bold{x = 5}$

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FIRST NO.

=> 3X

=> 3 * 5

$\huge\bold{15}$

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2ND NO.

=> 5X

=> 5 * 5

$\huge\bold{25}$

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HOPE HELPED .........

THANKS ........

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Answer 2

Ratio Of Numbers=3:5

Let Ratio=3x & 5x
If Each Increase By 10
3x+10
5x+10

Ratio Become=5:7

Ratio a:B can written as a/b

A/Q
$\frac{3x + 10}{5x + 10} = \frac{5}{7} \\ = 7(3x + 10) = 5(5x + 10) \\ = 21x + 70 = 25x + 50 \\ = 21x - 25x = 50 - 70 \\ = - 4x = - 20 \\ x = - \frac{ - 20}{ - 4} - \\ - - = + \\ = x = 5$
Numbers Are
3x=3×5=15
5x=5×5=25

Numbers
➡️15
➡️25