Question

A man received two shipments of ball bearings. In the first shipment, $1\%$ of the ball bearings were defective. In the second shipment which was twice as large as the first, $4.5\%$ of the ball bearings were defective. If the company received a total of $100$ defective ball bearings, how many ball bearings were there in the first shipment?

• A. $1500$
• B. $1200$
• C. $1000$
• D. $800$

Answer 1

Answer: (C)

$1000$

Let the number of ball bearings in the first shipment be $x$. Then the second shipment has been $2x$ ball bearings.
Given, $1$% of $x$ + $4.5$% of $2x=100$
$\frac{x}{100}+\frac{4.5}{100}\times 2x=100$

$\Rightarrow \frac{x}{100}+\frac{9x}{100}=100$

$\Rightarrow \frac{10x}{100}=100$

$x=1000$.