A consultancy allocated a total budget for a digital transformation project. In the first … — GMAT

A consultancy allocated a total budget for a digital transformation project. In the first phase, $\frac{3}{8}$ of the initial budget was spent. In the second phase, $40\%$ of the remaining budget was spent. If the unspent amount after both phases is $\$27,000$ , what was the initial budget of the project, in dollars?

Answer: 72000 dollars

Answer

72,000

To determine the initial budget, track the unspent fraction step by step. After the first phase,

\frac{5}{8}

of the budget remains. In the second phase,

40\%

(or

\frac{2}{5}

) of that remaining fraction is spent, which leaves

60\%

(or

\frac{3}{5}

) of the

\frac{5}{8}

unspent. Multiplying

\frac{3}{5} \times \frac{5}{8} = \frac{3}{8}

. Because

\frac{3}{8}

of the initial budget equals

\$27,000

, the full initial budget is

27,000 \times \frac{8}{3} = 72,000

Step-by-Step Solution

Find the fraction of the budget remaining after the first phase.

The fraction remaining after Phase 1 is

1 - \frac{3}{8} = \frac{5}{8}

The first phase spends

\frac{3}{8}

of the initial total budget.

Find the fraction of the total initial budget spent in the second phase.

Phase 2 expenditure =

40\% \times \frac{5}{8} = \frac{2}{5} \times \frac{5}{8} = \frac{2}{8}

40\%

is equivalent to

\frac{2}{5}

, which applies to the remaining

\frac{5}{8}

of the budget.

Determine the remaining fraction of the total budget after both phases.

Remaining fraction =

\frac{5}{8} - \frac{2}{8} = \frac{3}{8}

Subtracting the fraction spent in Phase 2 from the fraction left after Phase 1 yields the unspent portion.

Calculate the initial total budget in dollars.

Initial Budget =

\$27,000 \times \frac{8}{3} = \$72,000

Setting

\frac{3}{8}

of the total budget equal to the unspent amount of

\$27,000

determines the total.

Key Concept

Sequential fractional and percentage reductions from a base quantity

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