A banker spent \(\frac{1}{5}\) of his salary on shirts, \(\frac{1}{3}\) of the remainder on transport, and kept the rest for contingencies. What fraction was left
A
\(\frac{6}{15}\)
B
\(\frac{8}{15}\)
C
\(\frac{7}{15}\)
D
\(\frac{4}{5}\)
Verified Correct Answer: B.
Step-by-Step Mathematical Solution
Let the salary be \( S \).
Amount spent on shirts:
\(\text{Shirts} = \frac{1}{5} S\)
Remainder after shirts:
\(\text{Remainder} = S - \frac{1}{5} S = \frac{4}{5} S\)
Amount spent on transport:
\(\text{Transport} = \frac{1}{3} \left( \frac{4}{5} S \right) = \frac{4}{15} S\)
Remainder after transport:
\(\text{Remainder} = \frac{4}{5} S - \frac{4}{15} S = \frac{12}{15} S - \frac{4}{15} S = \frac{8}{15} S\)
Thus, the fraction left is: \(\frac{8}{15}\)
Source: WAEC / JAMB / NECO Classroom Archive (Record #74160)