There are two numbers in the ratio 8:9. if the smaller of the two numbers is increased by 12 and the larger number is reduced by 19 thee the ratio of the two numbers is 5:9.Find the larger number?

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venkat

  • Jul 29th, 2005
 

8x:9x initialy 
8x+ 12 : 9x - 19 = 5x:9x 
8x+12 = 5x  
-> x = 4 
9x = 36NOT SURE ABOUT THE ANSWER ..

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rajeshn

  • Dec 7th, 2005
 

X1:X2=8:9,(X1+12)*9=(X2-19)*5,9x1+108=5x2-95,9x1-5x2=-203,9x1=8x2,3x2=-203,x2=-203/3,x1=8x2/9,

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Partha006

  • Jun 30th, 2006
 

Venket you are wrong... we know that 8:2=4:1 but this doesnt meen that 8=4 wht you have done....

so the simplest solution is (8x+12)/(9x-19)=5/9.... solve it and get the value of 9x.. while solving i got some fraction value.. thus i think the values are not mentioned properly otherwise it is coming something near to 67

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vandana

  • Jul 21st, 2006
 

ya partha u are right but answer is coming in negative after solving the equation

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shivani

  • Oct 4th, 2006
 

yes friend i too got negative answer

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ramraj meena

  • Dec 30th, 2006
 

don't u think the ratio shold be reverse.........insteed of 5/9 it should be 9/5.........coz we increasing small number and reducing big number..............try itand solve

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don896

  • May 31st, 2010
 

Let Smallest number be x & largest number be y.
so X/y=8/9
x=8/9y

(x+12)/(y-19)=5/9

(8/9y+12)/(y-19)=5/9

8/9y^2-19*8/9y+12y-12*19-5/9=0

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Assume that: x is the small , y is the big
x / y = 8 / 9 --> x = 8y/9 (substitute by x in terms of y)
(X+12)/(y-19) = 5/9 --> (8y/9 + 12)/(y-19) = 5/9 --> 8y+108=5(y-19) --> y = (-95
– 108)/3 = -203/3


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ksrikant

  • Dec 19th, 2010
 

x:y=8:9 this means x is smaller than y(as x = (8/9)y). 

According to condition x+12/y-19 =5:9
9x+108 = 5y-95
but  9x=8y
so, 8y+108 = 5y-95
3y = -203
y= -203/3, which is the larger number.

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karthisiva

  • Dec 21st, 2010
 

(8/9)x*12/19=5/9,
sollution multiply 8 with 9 and 9 with 5,
so we get 72-45, and same for 12 and 19,
we get  27x=108-95,
x=13/27,
x=1/2.1,
largest  number =9*1/2.1
therfore the largest number is 4.5.

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