Arithmetic

Percentages

Easy

Out of the shirts produced in a factory, $15 \%$ are defective, while $20 \%$ of the rest are sold in the domestic market. If the remaining $8840$ shirts are left for export, then the number of shirts produced in the factory is

$13600$

$13000$

$13400$

$14000$

✅ Correct Option: 2

We work through this to understand how different percentages relate to each other.

We say the factory produces x shirts in total.

Here's what happens to these shirts:

15% are defective (these can't be sold)

The remaining 85% are good shirts that can be sold

Why 85%? Because if 15% are defective, then 100% - 15% = 85% are good.

Now, from these 85% good shirts:

20% are sold in the domestic market

The remaining 80% are exported

Why 80%? Because if 20% of the good shirts go to domestic market, then 100% - 20% = 80% of the good shirts are exported.

Here's the key insight: We need to find what percentage of the total production goes for export.

The exported shirts = 80% of the good shirts

The good shirts = 85% of total production

So, Exported shirts = 80% of 85% of total production

Converting to decimals: 0.80 × 0.85 = 0.68 = 68%

This means 68% of all shirts produced are exported.

We're told that 8840 shirts are exported.

Since exported shirts = 68% of total production:

68% of x = 8840

Converting percentage to fraction:

$\tfrac{68}{100} × x = 8840$

$x = 8840 × \tfrac{100}{68}$

$x = 8840 × \tfrac{25}{17}$

$x = \tfrac{8840 × 25}{17}

= \tfrac{221000}{17}

= 13000$

Therefore, the factory produces 13000 shirts.

When dealing with "percentage of percentage" problems, multiply the percentages to find the final percentage of the total.

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CAT Past Year Questions (Topic-Wise)

Out of the shirts produced in a factory, $15 \%$ are defective, while $20 \%$ of the rest are sold in the domestic market. If the remaining $8840$ shirts are left for export, then the number of shirts produced in the factory is