the ratio of numerator and denominator of the rational number is 2:7 and if 4 is added to the numerator and 2 is subtracted from the denominator the rational number becomes 10/19. find the original number
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Let the rational number be yx
Given, Denominator of rational number is 4 less than its numerator =>y=x−4=>x−y=4 --- (1)
Also, if 11is added to numerator and 1 is subtracted from denominator the new number, then number =y−1x+11=37
=>3x+33=7y−7
=>3x−7y=−40 --- (2)
Multiplying equation (1) with 3 we get, 3x−3y=12 ----- equation (3)
Subtracting equation (3)
from (2), we get 4y=52=>y=13
Substituting y=13 in the
equation (1), we get x=13=4=>x=17
Hence, the number is 1317
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