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A fraction becomes 31тАЛ when 1 is subtracted from the numerator and it becomes 41тАЛ when 8 is added to its denominator. The fraction is
127тАЛ
92тАЛ
31тАЛ
125тАЛ
None of the above
125тАЛ
Test the given options by substituting the numerator and denominator into the conditions: for 5/12, subtract 1 from 5 to get 4, then check 4/12 = 1/3 (Correct). Then add 8 to denominator 12 to get 20, check 5/20 = 1/4 (Correct).
A fraction x/y follows two conditions: (x-1)/y = 1/3 and x/(y+8) = 1/4.
yxтИТ1тАЛ=31тАЛ,y+8xтАЛ=41тАЛ
Test the given options by substituting the numerator and denominator into the conditions: for 5/12, subtract 1 from 5 to get 4, then check 4/12 = 1/3 (Correct). Then add 8 to denominator 12 to get 20, check 5/20 = 1/4 (Correct).
Many students subtract 1 from both the numerator and denominator or mix up the numerator/denominator operations.
Define the fraction
Let the fraction be yxтАЛ. Based on the problem, we have two equations.
yxтИТ1тАЛ=31тАЛтЯ╣y=3xтИТ3
Set up second equation
Using the second condition, add 8 to the denominator.
y+8xтАЛ=41тАЛтЯ╣4x=y+8
Solve the system
Substitute y=3xтИТ3 into 4x=y+8.
4x=(3xтИТ3)+8тЯ╣4xтИТ3x=5тЯ╣x=5
Calculate denominator
Substitute x=5 into y=3xтИТ3.
y=3(5)тИТ3=15тИТ3=12
D is correct because substituting x=5 and y=12 satisfies both conditions: (5-1)/12 = 4/12 = 1/3 and 5/(12+8) = 5/20 = 1/4.
This method of testing options (Back-Substitution) is often faster in competitive exams than solving algebraic equations, especially when the options are simple fractions.
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