Question

If \( t % \) of 40% of 100 is equal to 20% of 300, then the value of \( t \) is

• A. 150
• B. 155
• C. 125
• D. 225

Answer 1

The Correct Option is A

We are given the equation \( t\% \) of 40% of 100 is equal to 20% of 300. Let us first express both sides of the equation mathematically.

The left side is:
\[ \frac{t}{100} \times \left( 40\% \times 100 \right) = \frac{t}{100} \times 40 \]
Simplifying this:
\[ \frac{t}{100} \times 40 = \frac{40t}{100} = \frac{2t}{5} \]
The right side is:
\[ 20\% \times 300 = \frac{20}{100} \times 300 = 60 \]
Now we equate both sides of the equation:
\[ \frac{2t}{5} = 60 \]
Multiply both sides of the equation by 5 to eliminate the denominator:
\[ 2t = 60 \times 5 = 300 \]
Step 4: Divide both sides by 2 to solve for \( t \):
\[ t = \frac{300}{2} = 150 \]

To solve percentage problems, simplify the equation step by step, focusing on reducing percentages to decimals when necessary.