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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?

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? Correct Answer 2 hours

Let the usual speed be S.So, increased speed = $$\frac{{3{\text{S}}}}{2}$$Let usual time taken be TThus, 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 = 60ST = 120 minutes = 2 hoursAlternatively,As, ST = D Speed increase to $$\frac{{3}}{{2}}$$ times so time decreases to $$\frac{{2}}{{3}}$$ times . Net decrease = $$\frac{{1}}{{3}}$$ = 40 minutes.Hence actual time taken
= 3 × 40 = 120 mnts.
= 2 hours

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