A and B start running simultaneously. A runs from point P to point Q and B from point Q to point P. A's speed is 6/5 of B's speed. After crossing B, if A takes 5/2 hr to reach Q, how much time does B take to reach P after crossing A?
A thief steals a car and drives it at 15 km/hr. The theft has been discovered after one hour and the owner of the car sets off in another car at 25 km/hr. When will the owner overtake the thief from the starting point?
Answer: B Distance covered by the thief in one hour = 15 km Now this distance is to be covered by the relative speed of (25 -15) =10km/hr Hence, time required to cover this distance at a speed of 10km/hr = 15/10 = 1.5 hr.
Q. No. 27:
A hare sees a dog 200m away from her and scuds off in opposite direction at a speed of 24 km/hr. Two minutes later the dog perceives her and gives chase at a speed of 32km/hr. How soon will the dog overtake the hare, and what distance from the spot from where the hare took flight?
Answer: C Distance covered by hare in 2 min = 24/60 * 2 = 800m Now to overtake the hare dog has to cover a distance of (800+200) = 1000m with the relative speed of (32-24) = 8km/hr Time = 1/8 hr = 60/8 = 7.5 min. Now distance travelled by hare in 1/8 hr = 1/8 * 24 = 3km.
Q. No. 28:
A monkey tries to ascend a greased pole 14 m high. He ascends 2 m in first two minutes and slips 1 m in alternate minute. If he continues to ascend in this fashion, how long does he take to reach the top?
Answer: D In every two minutes he is able to ascend 1m. In this fashion he ascends upto 12m because when he reaches at the top he does not slip down. Thus, upto 12m he takes 12*2 = 24 min. and for the last 2 m he takes 1m. Therefore, total time taken by him is 24+1 = 25 min to reach the top.
Q. No. 29:
Jay started cycling along the boundaries of a square field from corner point A. After half an hour he reached the corner point C, diagonally opposite to A. If his speed was 8km/hr, the area of the filed in square km is
Answer: D Distance covered by Jay in 1/2 hr = 4km Therefore, side of the square = 4/2 = 2km Hence, Area = 2*2 = 4 square km.
Q. No. 30:
A hare, pursued by a grey-hound is 20 of her own leaps ahead of him. While the hare takes 4 leaps, the grey-hound takes 3 leaps. 3 leaps of grey-hound is equal to 2 leaps of hare. In how many leaps will the grey-hound overtake the hare?
Answer: A When hare takes 4 leaps, the grey-hound takes 3 leaps When grey hound takes 1 leap hare will take 4/3 leaps 3 leaps of grey-hound = 2 leaps of hare 1 leaps of grey-hound = 2/3 leaps of hare 4/3 leaps of hare = 4/3 * 2/3 leaps of grey-hound = 8/9 leaps Now the grey hound covers (1 - 8/9 = 1/9) leaps in his every leap. grey-hound covers 20 leaps in 20/(1/9) = 180 leaps.