Question

(a) U
(C)
()
d) 3
4. The ratio of two numbers is 5:9. If 9 is added to each number, then their
ratio becomes 16:27. Find the second number
71​

Answer 1

Answer:

The  second  number  is:  99

Step-by-step explanation:

      Let  the  numbers  be  x  and  y ;

Then:

   Given       x : y  =  5 : 9  ;

x / y  =  5 / 9  ;  

9x  =  5y ;

x = 5y / 9 ; ( equation  1 )

Given     (x + 9) / (y + 9)  =  16 / 27 ;

27( x + 9)  =  16( y + 9) ;

27x + 243  =  16y + 144 ;

 27 ( 5y/9 ) - 16 y  =  144  - 243 ;(From equation 1)

 15y - 16y  =  -99 ;

     -1y  =  -99 ;

     y =  99 ;

From equation  1 :

        x = 5y / 9 ;

        x = (5 * 99) / 9 ;

        x =  5 * 11 ;

        x =    55 ;

Therefore  the  first  number  is:    55

                  the  second  number  is:   99