Let a, b and c be the fractions such that a < b < c. If c is divided by a, the result is 5/2, which exceeds b by 7/4, If \(a + b + c = 1\frac{{11}}{{12}},\) then (c – a) will be equal to:
1/2
Step 1 — Find b: Since \(c/a=5/2\) exceeds b by 7/4,
\[b=\dfrac{5}{2}-\dfrac{7}{4}=\dfrac{10-7}{4}=\dfrac{3}{4}\]
Step 2 — Find a: With \(c=\tfrac{5}{2}a\) and \(a+b+c=\tfrac{23}{12}\):
\[a+\dfrac{3}{4}+\dfrac{5}{2}a=\dfrac{23}{12}\implies \dfrac{7}{2}a=\dfrac{14}{12}=\dfrac{7}{6}\]
\[a=\dfrac{1}{3},\quad c=\dfrac{5}{2}\cdot\dfrac{1}{3}=\dfrac{5}{6}\]
Therefore \(c-a=\dfrac{5}{6}-\dfrac{1}{3}=\dfrac{3}{6}=\mathbf{\tfrac{1}{2}}\).
Similar Questions
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Which of the following is correct?
Important Questions from Fractions
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Number 0.232323 can be written in rational form as:
Solve: \(\frac{1}{2}\) [{-2(2 + 3)*20}/2]
Match the following.
Column I
Column II
a.
Equivalent fraction of \(\frac{7}{12}\) is
i.
Proper fraction
b.
Equivalent fraction of \(\frac{9}{15}\) is
ii.
Improper fraction
c.
\(\frac{7}{11}\) is
iii.
\(\frac{21}{36}\)
d.
\(\frac{19}{5}\) is
iv.
\(\frac{3}{5}\)
Among the fractions \(\frac{7}{12}\) , \(\frac{8}{15}\) , \(\frac{17}{24}\) and \(\frac{13}{18}\) , which is the smallest?
