A student spent \frac{2}{5} of his monthly allowance on books and \frac{1}{3} of the remai… — JAMB UTME

A student spent $\frac{2}{5}$ of his monthly allowance on books and $\frac{1}{3}$ of the remaining amount on food. If he was left with $\text{N}4,000$ , what was his total monthly allowance in Naira ( $\text{N}$ )?

Answer: 10000 Naira

Answer

The total monthly allowance was 10,000 Naira.

After spending

\frac{2}{5}

on books,

\frac{3}{5}

of the allowance remains. Spending

\frac{1}{3}

of this remainder on food accounts for

\frac{1}{5}

of the original allowance. Subtracting

\frac{1}{5}

from

\frac{3}{5}

leaves

\frac{2}{5}

of the total allowance, which is equal to

\text{N}4,000

. Solving

\frac{2}{5} \times \text{Total} = 4,000

yields

10,000

Naira.

Step-by-Step Solution

Determine the remaining fraction after the first expenditure

Fraction left =

\frac{3}{5}

The student spent

\frac{2}{5}

on books, leaving

1 - \frac{2}{5} = \frac{3}{5}

of the total allowance.

Calculate the fraction of the total allowance spent on food

Fraction spent on food =

\frac{1}{5}

He spent

\frac{1}{3}

of the remaining

\frac{3}{5}

, which equals

\frac{1}{3} \times \frac{3}{5} = \frac{1}{5}

of the whole allowance.

Calculate the final remaining fraction of the allowance

Final fraction left =

\frac{2}{5}

The remaining fraction is

\frac{3}{5} - \frac{1}{5} = \frac{2}{5}

Solve for the total allowance

Total allowance = 10,000 Naira

Since

\frac{2}{5}

of the total allowance equals

\text{N}4,000

, the total allowance is

\frac{4,000 \times 5}{2} = 10,000

Naira.

Key Concept

Sequential Fraction of Remainder Problems

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