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 wa...

The key to solving this problem is to follow each step of the spending process, keeping track of what fraction of the salary is left after each transaction. We can use algebra to represent and simplify each step:

• Step 1: Spending on shirts
  The banker spends \( \frac{1}{5} \) of his salary on shirts.
  Let the whole salary be \( S \). The amount spent on shirts is \( \frac{1}{5}S \).
  That means the remainder is: \[ S - \frac{1}{5}S = \frac{4}{5}S \]

• Step 2: Spending on transport
  Next, the banker spends \( \frac{1}{3} \) of the remainder (which is \( \frac{4}{5}S \)) on transport:
  \[ \text{Amount spent on transport} = \frac{1}{3} \times \frac{4}{5}S = \frac{4}{15}S \]
  The new remainder (what he has left after transport) is: \[ \frac{4}{5}S - \frac{4}{15}S \] To subtract these, write both with a common denominator: \[ \frac{4}{5}S = \frac{12}{15}S \] \[ \frac{12}{15}S - \frac{4}{15}S = \frac{8}{15}S \]

• Step 3: Fraction left for contingencies
  At the end, the banker is left with \( \frac{8}{15} \) of his original salary.
  So the fraction left is \( \frac{8}{15} \).

Summary: The banker spends some money at each step, and each time the new amount spent is a fraction of what's left, not a fraction of the original salary. After both expenses, the fraction remaining is \( \frac{8}{15} \) of the starting salary.