# 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?

- 25%
- 50%
- 75%
- 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)

⇨ m^{2}/100 + n^{2}/100 = 2 mn / 100

Divide both sides by m^{2} and multiply by 100

So, 1 + (n/m)^{2} = 2(n/m)

Put (n/m) = x

So, x^{2} - 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.**