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Percentages

If 55% of ...

Question

If $55 %$ of $1000 + 60 %$ of $2000 = k : 2 k + 2$ , then find the sum of digits of $k$ .

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Solution

The correct option is C $2$
We have,
$\frac{55 % o f 1000}{60 % o f 2000} = \frac{k}{2 k + 2}$
$\Rightarrow \frac{55}{120} = \frac{k}{2 k + 2}$
$\Rightarrow 110 k + 110 = 120 k$
$\Rightarrow 10 k = 110 \Rightarrow k = 11$
$∴$ Sum of digits of $k = 1 + 1 = 2$

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