The sum of the numerator and denominator of a fraction is 11. If 1 is added to the numerator and 2 is subtracted from the denominator, it becomes $$\frac{2}{3}$$. The fraction is :
A. $$\frac{5}{6}$$
B. $$\frac{6}{5}$$
C. $$\frac{3}{8}$$
D. $$\frac{8}{3}$$
Answer: Option C
Solution(By Examveda Team)
Let the fraction be $$\frac{x}{y}$$Then,
$$\eqalign{ & \Leftrightarrow x + y = 11.....(\text{i}) \cr & \Leftrightarrow \frac{{x + 1}}{{y - 2}} = \frac{2}{3} \cr & \Leftrightarrow 3\left( {x + 1} \right) = 2\left( {y - 2} \right) \cr & \Leftrightarrow 3x - 2y = - 7.....(\text{ii}) \cr} $$
Solving (i) and (ii), we get:
x = 3 and y = 8
So, the fraction is $$\frac{3}{8}$$
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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