P, Q, R and S are four places. To travel from P to R, one travels via Q and to travel from P to S, one travels via both Q and R. Between P and Q, there are 3 routes; between Q and R, there are 4 routes; and between R and S, there are 5 routes. The time taken to travel through these routes is exhibited on the following chart in hours for a specific vehicle : How many possible routes are there if the journey takes exactly 7 hours?Routes Between P and Q Between Q and R Between R and S 1 2 1 2 2 3 1.5 2 3 4 2 2.5 4 - 2 3 5 - - 3.5
11
From the chart, the route times are: P–Q: 2, 3, 4 hours (3 routes); Q–R: 1, 1.5, 2, 2 hours (4 routes); R–S: 2, 2, 2.5, 3, 3.5 hours (5 routes). We need the number of route combinations (one from each stage) whose times add up to exactly 7 hours.
If P–Q = 2 hours, we need Q–R + R–S = 5: (1.5, 3.5) gives 1 way; (2, 3), using either of the two Q–R routes of time 2, gives 2 ways. Subtotal = 3.
If P–Q = 3 hours, we need Q–R + R–S = 4: (1, 3) gives 1 way; (1.5, 2.5) gives 1 way; (2, 2), using either of the two Q–R routes of time 2 matched with either of the two R–S routes of time 2, gives 2×2 = 4 ways. Subtotal = 1+1+4 = 6.
If P–Q = 4 hours, we need Q–R + R–S = 3: (1, 2), matched with either of the two R–S routes of time 2, gives 2 ways. Subtotal = 2.
Total number of routes = 3 + 6 + 2 = 11.
Similar Questions
There is a question followed by two statements I and II :
Question :
If x and y are integers, can we find |x-y| uniquely?
I. x2 + y2 = 25
II. x2 - y2 = 7
Which one of the following options is correct?
Important Questions from Quant Based Puzzle
A number is subtracted from 4 times of it and then, the number obtained is added to its (the resultant’s) next number. If this gives the answer as 91, what was the original number?
When twice of a number added to 3 is multiplied by 5 and added to the number itself, it gives 158. What is the square of that number?
In a class of 72 students, the number of boys is twice the number of girls. Find the number of boys.
Two years ago, T was twice as old as P. P is thrice as old as R. In five years, P will be 29. What is the present age of T?
When a number is added to its multiple of 5 and its square, the sum of these three numbers is 91. Find the number.
