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# If 2 is added to each of two given numbers, their ratio becomes 1:2 However, if 4 is substracted from each of the given numbers, the ratio becomes 5:11 Find the numbers.

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Here the ratio of two numbers when the given number is added and substracted from each of the given numbers
is given. You have to find the numbers.
This is the Important question based on Linear Equations in two Variables Chapter of R.S Aggarwal book for
ICSE & CBSE Board.
This is the Question Number 9 Of Exercise 3E of RS Aggarwal Solution.

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1. Let x and y be the two numbers.

according to the question,
If 2 is added to each of two given numbers, their ratio becomes 1:2.
=> ( (x + 2) / ( y+2) ) = 1/2
=> 2x – y = – 2
=> y = 2x + 2…………………………………………….(1)

if 4 is subtracted from each of the given numbers, the ratio becomes 5:11.
=> ( ( x – 4 ) / ( y-4 ) ) = 5 /11
=> 11x – 5y= 24………………………………………(2)

substituting the value of y from eq (1) in eq(2) , we get
=> 11 x – 5( 2x+2) = 24
=> 11x – 10x  = 34
=> x= 34

y = 2x + 2
=> y = 2(34) +2 = 68 + 2
=> y = 70

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