Question 43

If S =$$\frac{3T}{2}$$ , then express 'T' as a percentage of S + T.

Given $$S = \frac{3T}{2}$$.

Re-arrange to express $$T$$ in terms of $$S$$:
$$3T = 2S \; \Longrightarrow \; T = \frac{2S}{3}$$.

Now find the fraction of $$T$$ with respect to $$S+T$$:
$$\frac{T}{S+T} = \frac{\frac{2S}{3}}{S + \frac{2S}{3}}$$.

Simplify the denominator first:
$$S + \frac{2S}{3} = \frac{3S + 2S}{3} = \frac{5S}{3}$$.

Hence,
$$\frac{T}{S+T} = \frac{\frac{2S}{3}}{\frac{5S}{3}} = \frac{2}{5}$$.

Convert this fraction to a percentage by multiplying by $$100$$:
$$\frac{2}{5} \times 100 = 40\%$$.

Therefore, $$T$$ is $$40\%$$ of $$S + T$$.
Option B which is: 40%.

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