Question

Two numbers are in ratio 3:5. If 9 is subtracted from each, then they are in the ratio of 12:23. Find the second number.
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Answer 1

Answer:

smaller number would be 33

Step-by-step explanation:

Let the numbers be x & y, then as per given :

x/y= 3/5

or, 5x-3y=0 ———(i)

& x-9/y-9=12/23

or, 23(x-9)= 12(y-9)

or, 23x-12y=23×9–12×9= 99———-(ii)Now, multiplying (i) & (ii) bothsides by 4 & 1 respectively, we get:

20x-12y=0——(iii)

& 23x-12y=99——(iv)

Now, by deducting (iii) from(iv), we get:

3x=99

or, x=99/3=33

Now, putting this value of x in either of the equations, we get:

5×33–3y=0

or, 3y= 165

or, y=165/3=55

Hence, the smaller number would be 33

Answer 2

let the number ne 3x and 5x

according to the question

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

cross multiply

$23(3x - 9) = 12(5x - 9) \\ \frac{23 \times 3x}{23 \times 9} = \frac{12 \times 5x}{12 \times 9} \\ 69x - 207 = 60x - 108 \\ 9x = 99 \\ x = \frac{99}{9} \\ x = 11$

Second no. = 5 × 11 = 55