Question

two numbers are in the ratio of 3:5 if 9 is subtracted from each the new numbers are in the ratio 12:23 the smaller number is?

Answer 1

Answer:

Smaller number = 33

Bigger number = 55

Step-by-step explanation:

Let the numbers in the ratio 3 : 5 be 3x and 5x

If 9 subtracted from each of them, the numbers becomes 3x - 9 and 5x - 9

When 9 subtracted from 3x and 5x, the ratio of the numbers becomes 12 : 23.

According to the question,

$\dfrac{3x - 9}{5x - 9}$ = $\dfrac{12}{23}$

23(3x - 9) = 12(5x - 9)

69x - 207 = 60x - 108

69x - 60x = 207 - 108

9x = 99

x = $\dfrac{99}{9}$

x = 11

1st number => 3x

=> 3 * 11

=> 33

2nd number => 5x

=> 5 * 11

=> 55

∴ The smaller number is 33 and the bigger number is 55 respectively.

Answer 2

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▶ Question - Two numbers are in the ratio of 3:5 if 9 is subtracted from each the new numbers are in the ratio 12:23 the smaller number is?



▶ Explanation :-



Given two numbers are in the ratio 3 : 5



Let the smaller number be 3x



Larger number be 5x



Given 9 is subtracted from each numbers the new numbers are in the ratio 12 : 23



According to the Question :-



=> 3x - 9 / 5x - 9 = 12 / 23


=> 23 ( 3x - 9 ) = 12 ( 5x - 9 )


=> 69x - 207 = 60x - 108


=> 69x - 60x = - 108 + 207


=> 9x = 99


=> x = 99 / 9


=> x = 11



∴ The smaller number = 3x


= 3 × 11


= 33


∴ The smaller number =33



∴ The Larger number = 5x


= 5 × 11


= 55


∴ The Larger number = 55




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