When a person goes to his office from his house with a speed of 10 km/hr, he is late by 20 minutes. When he goes with speed of 15 km/hr, he is late by 5 minutes. What is the distance (in km) between his office and house?

Let ideal time taken be $$t$$ hours

Since, speed is inversely proportional to time,

=> $$\frac{10}{15}=\frac{t+\frac{5}{60}}{t+\frac{20}{60}}$$

=> $$10t+\frac{10}{3}=15t+\frac{5}{4}$$

=> $$5t=\frac{10}{3}-\frac{5}{4}$$

=> $$5t=\frac{40-15}{12}=\frac{25}{12}$$

=> $$t=\frac{5}{12}$$ hours

$$\therefore$$ Distance = speed $$\times$$ time

= $$10\times(\frac{5}{12}+\frac{20}{60})$$

= $$10\times\frac{45}{60}=7.5$$ km

=> Ans - (B)