# GATE Mechanical 2022 Set 2 | GA Question: 9

1 vote

Four cities $\text{P, Q, R}$ and $\text{S}$ are connected through one-way routes as shown in the figure. The travel time between any two connected cities is one hour. The boxes beside each city name describe the starting time of first train of the day and their frequency of operation. For example, from city $\text{P}$, the first trains of the day start at $8\;\text{AM}$ with a frequency of $90$ minutes to each of $\text{R}$ and $\text{S}$. A person does not spend additional time at any city other than the waiting time for the next connecting train.

If the person starts from $\text{R}$ at $7\;\text{AM}$ and is required to visit $\text{S}$ and return to $\text{R}$, what is the minimum time required?

1. $6$ hours $30$ minutes
2. $3$ hours $45$ minutes
3. $4$ hours $30$ minutes
4. $5$ hours $15$ minutes

recategorized

If the person starts from $\text{R}$ at $\text{7 AM}$ and is required to visit $\text{S}$ and return to $\text{R},$ then he must visit $\text{Q}$ and $\text{P}$ in between.

$\underbrace{\underbrace{\text{R}}_{{\color{Green}{\text{Start at: 7 AM}}}} \overset{\text{1 hour}}{\Longrightarrow} {\underbrace{\text{Q}}_{{\color{Red}{\text{Next train at: 9 AM}}}}} \overset{\text{1 hour}}{\Longrightarrow} \underbrace{\text{P}}_{{\color{Blue}{\text{Next train at: 11 AM}}}} \overset{\text{1 hour}}{\Longrightarrow} \underbrace{\text{S}}_{{\color{Purple}{\text{Next train at: 12:30 PM}}}} \overset{\text{1 hour}}{\Longrightarrow} \underbrace{\text{R}}_{{\color{Lime}{\text{Reach at: 1:30 PM}}}}}_{\text{Total time taken by person = 1 + 1 (waiting) + 1 + 1 (waiting) + 1 + ½ (waiting) + 1 = 6:30 hours}}$

$\therefore$ If the person starts from $\text{R}$ at $\text{7 AM}$ and is required to visit $\text{S}$ and return to $\text{R},$ then the minimum time required is $\text{6 hours 30 minutes}.$

Correct Answer $:\text{A}$

6.9k points 3 6 14
edited

## Related questions

Fish belonging to species $S$ in the deep sea have skins that are extremely black (ultra-black skin). This helps them not only to avoid predators but also sneakily attack their prey. However, having this extra layer of black pigment results in lower ... and disadvantages to species $S$ Having ultra-black skin is only disadvantageous to species $S$ but advantageous only to their predators
Four girls $\text{P, Q, R and S}$ are studying languages in a University. $P$ is learning French and Dutch. $Q$ is learning Chinese and Japanese. $R$ is learning Spanish and French. $S$ is learning Dutch and Japanese. Given that: French is easier than Dutch; ... is easier than French. Based on the above information, which girl is learning the most difficult pair of languages? $P$ $Q$ $R$ $S$
Given below are three conclusions drawn based on the following three statements. Statement $1$ : All teachers are professors. Statement $2$ : No professor is a male. Statement $3$ : Some males are engineers. Conclusion $\text{I}$: No engineer is a professor. ... conclusion $\text{II}$ and conclusion $\text{III}$ are correct Only conclusion $\text{I}$ and conclusion $\text{III}$ are correct
If $\bigoplus \div \bigodot =2;\: \bigoplus \div\Delta =3;\:\bigodot +\Delta =5; \:\Delta \times \bigotimes =10$, Then, the value of $\left ( \bigotimes - \bigoplus \right )^{2}$, is : $0$ $1$ $4$ $16$
Given below are two statements $1$ and $2$, and two conclusions $\text{I}$ and $\text{II}$. $\text{Statement 1}:$ All entrepreneurs are wealthy. $\text{Statement 2}:$ All wealthy are risk seekers. $\text{Conclusion I}:$ ... $\text{I}$ nor $\text{II}$ is correct Both conclusions $\text{I}$ and $\text{II}$ are correct