Mr A started half an hour later than usual for the marketplace. But by increasing his speed to $$\frac{3}{2}$$ times his usual speed he reached 10 minutes earlier than usual. What is his usual time for this journey?
a) 1 hours
b) 2 hours
c) 3 hours
d) 45 minutes
Answer: b
Explanation: Let the usual speed be S.
increased speed = $$\frac{{3{\text{S}}}}{2}$$
Let usual time taken be T
Thus, S × T = D, and also $$\frac{{3{\text{S}}}}{2}$$ × (T – 40) = D. (T – 40, Because he started 30 minutes later and reached 10 minutes earlier, means he saved 40 minutes)
$$\frac{{3{\text{S}}}}{2}$$ × (T – 40) = ST
$$\frac{{3 \times {\text{ST}}}}{2}$$ – 60S = ST
$$\frac{1}{2}$$ × ST = 60S
T = 120 minutes = 2 hours
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