If m% of m + n% of n = 2% of (m × n)

• Percentages

If m% of m + n% of n = 2% of (m × n), then what percentage of m is n?

1. 25%
2. 50%
3. 75%
4. 100%

Answer

We need to calculate the ratio n/m.

According to the question, we have:

(m/100) × m + (n/100) × n = 2/100 × (mn)

⇨ m²/100 + n²/100 = 2 mn / 100  

Divide both sides by m² and multiply by 100

So, 1 + (n/m)² = 2(n/m)

Put (n/m) = x 

So, x² - 2x + 1 = 0

 ⇨ (x - 1)² = 0

⇨ x = 1

So, x = n/m = 1

⇨ n = m

Therefore, n is (100% of m) or equal to m.

The correct option is D.