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In a fraction, if the numerator is decreased by 1 and the denominator is increased by 1, then the fraction becomes 1/2. Instead, if the numerator is increased by 1 and the denominator is decreased by 1, then the fraction becomes 4/5. Find the numerator of the fraction.A) 2 B) 7 C) 4 D) 10 |
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Answer» Correct option is (B) 7 Let the required fraction be \(\frac xy.\) According to first condition, we have \(\frac{x-1}{y+1}=\frac12\) \(\Rightarrow\) 2x - 2 = y + 1 (By cross multiplication) \(\Rightarrow\) 2x - y - 3 = 0 ___________(1) According to second condition, we have \(\frac{x+1}{y-1}=\frac45\) \(\Rightarrow\) 5 (x+1) = 4 (y - 1) (By cross multiplication) \(\Rightarrow\) 5x + 5 = 4y - 4 \(\Rightarrow\) 5x - 4y + 9 = 0 ___________(2) Multiply equation (1) by 4, we get 8x - 4y - 12 = 0 ___________(3) Subtract equation (2) from (3), we get (8x - 4y - 12) - (5x - 4y + 9) = 0 - 0 \(\Rightarrow\) 3x - 21 = 0 \(\Rightarrow\) x = \(\frac{21}3\) = 7 Hence, the numerator of fraction \(\frac xy\) is x = 7. Correct option is B) 7 |
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