Quant Boosters  Shashank Prabhu, CAT 100 Percentiler  Set 7

Q26) Ramesh and Shyam are competing in 2000 m race. Ramesh gives Shyam a lead of 200 m . Initially Ramesh runs at 4 times Shyam’s speed, but after crossing the 1200 m mark, he slows down to 1/8th of this initial speed, while Shyam continues to run at his original speed. If Ramesh and Shyam meet for the second time at distance ‘a’ m from the finishing line then find ‘a’.

Let Ramesh be 40 m/s, Shyam be 10 m/s. Ramesh reaches 1200 m after 30 seconds. Shyam covers 300 m in that time. New speed of Ramesh is 5 m/s, distance between Ramesh and Shyam is 700 m. So, they meet after 140 seconds. Shyam covers 1400 m more in this time period. So, total of 1900 m from the start or 100 m from the end.

Q27) A pool is fitted with 3 pipes. The first 2 pipes operating simultaneously fill the pool in the same time during which the pool is filled by the third pipe alone. The second pipe fills the pool 5 hours faster than the first pipe and 4 hours slower than the third pipe. Find the time required by third pipe to fill the pool.
a. 12 hours
b. 10 hours
c. 8 hours
d. 6 hours

Let B fill it in x hours.
(1/x) + (1/(x + 5)) = 1/(x  4).
On solving, we get x = 10. So, x  4 = 6 hours.

Q28) Arun buys a certain number of cards, pads, and DVD’s. 2 DVD’s and 2 pads together can be bought for the cost of 3 cards. If each card had cost Rs. 8 more, then each card would have been worth either 2 DVD’s or 7 pads. The sum of the cost of one pair of each (in units) is

2d + 2p = 3c
c + 8 = 2d = 7p
On substitution, we get c = 6, d = 7, p = 2.
As one pair of each is asked, it will be 2 * (6 + 7 + 2) = Rs. 30

Q29) If 2 men can do a work in the same time as can 3 women or 4 children, how many days will it take for 3 men, 4 women and 5 children to do a job which four men take 98 days to complete?

2m = 3w = 4c
4 men do it in 98 days. So, total work is 392m.
3m + 4w + 5c = 3m + 8m/3 + 5m/2 = 49m/6 per day.
Number of days = 392*6/49 = 48 days.

Q30) Santosh was the guest speaker at a seminar on “Careers After Class XII” at the Cummins College of Engineering. He left his office and travelled at a certain speed so that he would reach the college on time. After travelling half the distance, he realised that he had left his laptop in office. He turned back immediately and increased his speed by 50% and reached his office. As compared to his original speed, by what percent should Santosh increase his speed so that he still reaches the college on time?

100 km in 10 hours at 10 km/hr. 50 km in 5 hours covered. 50 km back at 15 km/hr in 10/3 hours. 100 km to be covered in 5/3 hours at 60 km/hr. Increase by 500%