Walking $$\frac{3}{4}$$ of his normal speed, Rabi is 16 minutes late in reaching his office. The usual time taken by him to cover the distance between his home and office:

Walking $$\frac{3}{4}$$ of his normal speed, Rabi is 16 minutes late in reaching his office. The usual time taken by him to cover the distance between his home and office: Correct Answer 48 min.

1^st method:$$\frac{4}{3}$$ of usual time = Usual time + 16 minutes;Hence, $$\frac{1}{3}{\text{rd}}$$  of usual time = 16 minutes;Thus, Usual time = 16 × 3 = 48 minutes.2^nd method:When speed goes down to$$\frac{3}{4}{\text{th}}$$  (i.e. 75%) time will go up to $$\frac{4}{3}{\text{rd}}$$  (or 133.33%) of the original time.Since, the extra time required is 16 minutes; it should be equated to $$\frac{1}{3}{\text{rd}}$$  of the normal time.Hence, the usual time required will be 48 minutes.