## Quantitative Questions

Answer the following two questions Q1. A candidate is required to answer exactly 6 out of 10 questions divided into two groups, each containing 5 questions. He is not permitted to attempt more than 4 from each group. In how many ways can he made up his choice? a. 2^6 b. 200 c. 300 d. None of these Q2. A and B start from the same point to run in opposite directions round a circular path of 550 yards in length. A gives B a start of 100 yards. They pass each other when A has run 250 yards. Who will come first to the starting point and what distance would they be apart then? a. A, 10 yards b. B, 10 yards c. A, 20 yards d. None of these

## Solution to Question 2

Q2. A and B start from the same point to run in opposite directions round a circular path of 550 yards in length. A gives B a start of 100 yards. They pass each other when A has run 250 yards. Who will come first to the starting point and what distance would they be apart then? a. A, 10 yards b. B, 10 yards c. A, 20 yards d. None of these Solution: It is given that A has given B a lead of 100 yards and they both meet when A has covered 250 yards. Now, it is clear that when they both meet, the total distance covered by both A and B is 550 yards and so B has only covered 200 yards when A has covered 250 yards. So, from here we now know that A has to cover 300 yards more to reach the starting point and B has to cover 250 yards to reach at the starting point. Since when A covers 250 yards, B covers 200 yards, we can also conclude that the ratio of the speeds of A and B is 5 : 4. This means: When A covers 5 yards, B covers 4 yards. So, when A covers 300 yards, B will cover 240 yards. Now A has reached the starting point and B has covered (300 + 240) yards = 540 yards. Hence A reaches the starting point first and they would then be 10 yards apart. [Option (a)] Thank You Ravi Raja

## Solution to Question 1

Q1. A candidate is required to answer exactly 6 out of 10 questions divided into two groups, each containing 5 questions. He is not permitted to attempt more than 4 from each group. In how many ways can he made up his choice? a. 2^6 b. 200 c. 300 d. None of these Solution: The number of ways in which he can do this is: Attempt 2 Questions from Group I and 4 Questions from Group II, which can be done in 5C4 x 5C2 ways = 50 ways Attempt 3 Questions from Group I and 3 Questions from Group II, which can be done in 5C3 x 5C3 ways = 100 ways Attempt 4 Questions from Group I and 2 Questions from Group II, which can be done in 5C2 x 5C4 ways = 50 ways Hence the total number of ways is: 50 + 100 + 50 = 200 ways. [Option (b)] Thank You Ravi Raja