Question

Two numbers are in the ratio of 3:5.if 9 is subtracted from each then they
become 12:23. Find the numbers?
a )23,46
b) 33,55
c )32,16
d) 13,28​

Answer 1

Answer:

Two numbers are in the ratio of 3:5.

Let the two numbers be 3x, 5x

9 is subtract from each

3x - 9 , 5x - 9 => 12 :23

3x -9 = 12

3x = 12+9

3x = 21

x = 21/3 = 7

5x - 9 =23

5x = 23+9

5x = 32

x = 32/5

Now 3x = 3 * 7 = 21

5x = 5 * 32 /5 = 32

Numbers are = 21:35

Verification :- subtract 9 from both the numbers

21-9 = 12

32-9 = 23

Answer 2

$\mathcal{\huge{\underline{\purple{Question:-}}}}$

Two numbers are in the ratio of 3:5. If 9 is subtracted from each, then they become 12:23. Find the numbers.

a) 23,46

b) 33,55 ✔︎

c) 32,16

d) 13,28

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Given :-

• Two numbers are in the ratio 3:5.

• 9 is subtracted from each, they become 12:23

To Find :-

• Those numbers.

__________________________

$\mathcal{\huge{\underline{\purple{Solution:-}}}}$

Put x in the ratio

Then,

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

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

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

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

$= > 9x = 99$

$= > x = \frac{99}{9}$

$= > x = 11$

Put the value of x in the ratio.

$3 \times x = 3 \times 11 = 33$

$5 \times x = 5 \times 11 = 55$

Hence, these numbers are 33 and 55.

Therefore option b) is correct.

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