If the numerator of a fraction is increased by 2 and the denominator is increased by 3, the fraction becomes $$\frac{7}{9}$$ and if both the numerator as well as he denominator are decreased by 1, the fraction becomes $$\frac{4}{5}$$. What is the original fraction ?
A. $$\frac{5}{6}$$
B. $$\frac{9}{11}$$
C. $$\frac{13}{16}$$
D. $$\frac{17}{21}$$
Answer: Option A
Solution(By Examveda Team)
Let the fraction be $$\frac{x}{y}$$Then,
$$\eqalign{ & \Leftrightarrow \frac{{x + 2}}{{y + 3}} = \frac{7}{9} \cr & \Leftrightarrow 9x - 7y = 3.....(i) \cr & {\text{And,}} \cr & \Leftrightarrow \frac{{x - 1}}{{y - 1}} = \frac{4}{5} \cr & \Leftrightarrow 5x - 4y = 1.....(ii) \cr} $$
Solving (i) and (ii), we get :
x = 5 and y = 6
Hence, the original fraction is $$\frac{5}{6}$$
Related Questions on Problems on Numbers
If one-third of one-fourth of a number is 15, then three-tenth of that number is:
A. 35
B. 36
C. 45
D. 54
E. None of these
A. 9
B. 11
C. 13
D. 15
E. None of these
A. 3
B. 4
C. 9
D. Cannot be determined
E. None of these
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