A wholesale distributor imported a batch of organic green tea leaves. On Monday, 30\% of t… — GMAT

A wholesale distributor imported a batch of organic green tea leaves. On Monday, $30\%$ of the initial batch was sold. On Tuesday, $\frac{4}{7}$ of the remaining batch was sold. If the distributor had $126$ kilograms of green tea leaves left at the end of Tuesday, what was the total weight, in kilograms, of the initial batch imported?

A
$294$
B
$315$
$420$ Answer
D
$700$
E
$980$

Answer

The total weight of the initial batch imported was

420

kilograms.

Selling

30\%

on Monday leaves

70\%

of the initial total. On Tuesday, selling

\frac{4}{7}

of that remaining amount leaves

\frac{3}{7}

of the

70\%

. Calculating

\frac{3}{7} \times 70\% = 30\%

. Since

30\%

of the initial batch is equal to

126

kg, the total initial weight is

126 \div 0.30 = 420

kg.

Step-by-Step Solution

Determine the fraction of the initial batch remaining after Monday's sale.

Since

30\%

(

0.30

) was sold,

1 - 0.30 = 0.70

(or

\frac{7}{10}

) of the initial batch remained.

Percentage decreases are calculated relative to the original whole.

Determine the fraction of Monday's remaining batch that was left after Tuesday's sale.

Since

\frac{4}{7}

of Monday's remainder was sold,

1 - \frac{4}{7} = \frac{3}{7}

of Monday's remainder was left.

Subsequent fractional sales are relative to the updated intermediate amount.

Calculate the final remaining amount as a fraction of the initial total weight

W

\text{Final Remaining} = \frac{3}{7} \times \left(\frac{7}{10} W\right) = \frac{3}{10} W = 0.30 W$.

Multiplying successive remaining ratios gives the net remaining fraction of the original batch.

Solve for the initial weight

W

using the given remaining weight of

126

kg.

0.30 W = 126 \implies W = \frac{126}{0.30} = 420\text{ kg}.

Dividing the remaining weight by its corresponding decimal fraction yields the total initial weight.

Key Concept

Successive percentage and fractional reductions require applying each change to the updated intermediate base value rather than the original total.

Estimated Time:1m 30s

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