A car overtakes a bus travelling from Delhi to Jaipur at 4 : 30 p.m. The car reaches Jaipur at 6 : 00 p.m… · ABC26GN3760
Subject: General Aptitude · Chapter: Time and Distance
A car overtakes a bus travelling from Delhi to Jaipur at 4 : 30 p.m. The car reaches Jaipur at 6 : 00 p.m. After stopping there for 1 hour, it starts back towards Delhi and meets the same bus at 7 : 30 p.m. which was moving towards Jaipur at that time. If both the bus and the car were travelling with uniform speeds on the same route, at what time would the bus reach Jaipur?
(a)8 : 30 p.m.
(b)9 : 00 p.m.
(c)9 : 15 p.m.
(d)9 : 30 p.m.
Answer
Answer (as printed): B
Explanation
Suppose after meeting the bus, the car travelled $x \mathrm{km}$ to reach Jaipur. Then, it travelled $x \mathrm{km}$ in $1 \frac{1}{2}$ hours. Again, it travelled back to meet the bus again in $1 \frac{1}{2}$ hours. Now, distance travelled in $\frac{1}{2}$ hour $=\frac{x}{3} \mathrm{km}$. The bus travelled $\left(x-\frac{x}{3}\right)=\frac{2 x}{3} \mathrm{km}$ in 3 hours. So, it will travel $x \mathrm{km}$ in $\left(3 \times \frac{3}{2 x} \times x\right) \mathrm{hrs}=\frac{9}{2} \mathrm{hrs}=4 \frac{1}{2} \mathrm{hrs}$. Hence, the bus will reach Jaipur $4 \frac{1}{2}$ hours after 4 : 30 p.m. i.e. at 9 p.m.