Question

two numbers are such that there ratio is 5:6 if each is increased by 9 the ratio between two numbers bocomes 89. find the orginal number.

Answer 1

Let original Numbers would be 5x and 6x,



Given in the question that if each increases by 9 then the new ratio becomes 8 : 9


Converting the theory in equation,





$\frac{5x + 9}{6x + 9} = \frac{8}{9} \\ \\ \\ = > 9(5x + 9) = 8(6x + 9) \\ \\ \\ = > 45x + 81 = 48x + 72 \\ \\ \\ = > 81 - 72 = 48x - 45x \\ \\ \\ = > 9 = 3x \\ \\ \\ \frac{9}{3} = x \\ \\ \\ = > 3 = x$




Hence, Original numbers are 5x = 5( 3 ) = 15 and 6x = 6( 3 ) = 18

Answer 2

» let's the two numbers are "x" and "y"

Now

» accordin to the question :-

=> x : y = 5 : 6

=> x/y = 5/6

=> y = 6x/5 _______eq(1)

________________

» and also given that if each is increasing by 9 the ratio will be 8 : 9

then

=> (x+9) : (y+9) = 8 : 9

=> (x+9)/(y+9) = 8/9 _____[eq(2)]

_____________

» by eq(1) and eq(2)

$= > \frac{x + 9}{ \frac{6x}{5} + 9 } = \frac{8}{9} \\ \\ = > \frac{5x + 45}{6x + 45} = \frac{8}{9} \\ \\ = > \frac{5x + 45}{2x + 15} = \frac{8}{3} \\ \\ = > 15x + 135 = 16x + 120 \\ \\ = > x = 15$

then.

by eq(1) :-

$= > y = \frac{6x}{5} \\ \\ = > y = \frac{6 \times 15}{5} = 18$

_______-__________

» HENCE the original number are "15 and 18"

_______________[ANSWER]

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