The Official CAT 2007 Quant Thread

[gautamgomzi]

Q. Two Indian tourist in the US cycled towards each other, one from point A and other from point B. The first tourist left point A six hours later than the second tourist left B, and it turned out on their meeting that he had traveled 12 km less than the second tourist. After their meeting, they kept cycling with the same speed and the first tourist arrived at B 8 hours later and the second arrives at A 9 hours later.Find the speed of the faster tourist.ANS - 4kmph-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------Q. Two joggers left Delhi for Noida simultaneously. The first jogger stopped 42 min later when he was 1 km short of Noida and the other one stopped 52 min later when he was 2 km short of Noida. If the first jogger jogged as many kilometers as the second jogger and the second as many kilometer as the first, the first one would need 17 min less than the second. Find the distance between Delhi & Noida ?ANS – 15 km

[dashing]

Originally Posted by gautamgomzi

Q. Two Indian tourist in the US cycled towards each other, one from point A and other from point B. The first tourist left point A six hours later than the second tourist left B, and it turned out on their meeting that he had traveled 12 km less than the second tourist. After their meeting, they kept cycling with the same speed and the first tourist arrived at B 8 hours later and the second arrives at A 9 hours later.Find the speed of the faster tourist.ANS - 4kmph

Hi

the equations is formed are

(x+12)/b - x/a = 6
(x+12)/a = 8
x/b = 9

so solving them

x = 36
so b = 4
a = 6

So the speed of the faster tourist is 6
but its given 4

[dashing]

Originally Posted by gautamgomzi

Q. Two joggers left Delhi for Noida simultaneously. The first jogger stopped 42 min later when he was 1 km short of Noida and the other one stopped 52 min later when he was 2 km short of Noida. If the first jogger jogged as many kilometers as the second jogger and the second as many kilometer as the first, the first one would need 17 min less than the second. Find the distance between Delhi & Noida ?ANS – 15 km

the equations formed

(x-1)/a = 42
(x-2)/b = 52
(x-1)/b - (x-2)/a = 17

Solving them

x = 15

[implex]

Originally Posted by dashing

Hi

the equations is formed are

(x+12)/b - x/a = 6
(x+12)/a = 8
x/b = 9

so solving them

x = 36
so b = 4
a = 6

So the speed of the faster tourist is 6
but its given 4

let the two meet at point c
and speeds of A be x and that of B be y
AC=9y and BC=8x

8x-9y=12
and
8x/y-9y/x=6

solve it for x u get x=6
and y=4

so faster is 6

wrong answer given

[gautamgomzi]

Q. An ant climbing up a vertical pole ascends 12 metre and slips down 5 metre in every alternate hour. If the Pole is 63m high how long will it take to reach the top ?ANS- 16 hr 35 minutes**************************************Q. Ravi, who lives in the countryside, caught a train for home earlier than usual yesterday. His wife normally drives to the station to meet him. But yesterday he set out on foot from the station to meet his wife on the way. He reached home 12 min earlier than he would have done had he waited at the station for his wife. The car travels at a uniform speed, which is 5 times Ravi’s speed on foot. Ravi reached home exactly at 6 o’clock. At what time would he have reached home if his wife, forewarned of his plan, had met him at the station ?ANS- 5:36********************************************** *****Q. Hemant and Ajay start a two-length swimming race at the same moment but from opposite ends of the pool. They swim in lane and at uniform speeds, but hemant is faster than Ajay. They first pass at a point 18.5 metre from the deep end and having completed one length, each one is allowed to rest on the edge for exactly 45 seconds. After setting off on the return length, the swimmers pass for the second time just 10.5 m from the shallow end. How long is the pool?ANS – 45 metre*******************************************Q. Rahim sets out to cross a forest. On the first day, he completes 1/10th of the journey. On the second day, he covers 2/3rd of the distance traveled the first day. He continues in this manner, alternating the days in which he travels 1/10th of the distance still to be covered, with days on which he travels 2/3rd of the total distance already covered. At the end of the 7th day he finds that 22½ km more will see the end of his journey. How wide is the forest?ANS - 120km********************************************* ******Q. Two people A and B start from P and Q (distance = D) at the same time towards each other. They meet at a point R which is at a distance 0.4D from P. They continue to move to and fro between the two points. Find the distance from point P at which the fourth meeting takes place ?ANS- 0.8D********************************************** **Plz help me with these probz...GK

[implex]

ah u have messed up the questions ayways

the first one is clearly simple
now we can clealry see he will end up at (12-5)*8=56 m at teh end of 16 hours
now he can reach 7 meters remaining in the 35 more mins .. he need not fall :P

so teh time is 16 hours and 35 mins

[implex]

for teh second one assume
that the distance betwwen home and station is y
and the speeds are 5x and x
and also that ravi has to wait for z mins

suppose he would have waited for z mins then total time taken will be z+ time taken by car=z+y/5x

if he does not wait
so his wife is 5xz distance away from the station..
so she reaches him in 5xz/(5x+x)=5z/6
now time to go back is (y-5xz+5x.5z/6)/5x=y/5x-z/6
so total time in second case is =5z/6+y/5x-z/6

in this case we get
z+y/(5x)=5z/6+ y/(5x)-z/6+12( given he reaches 12 min earlier)
z=18 mins

clealry the time saved now is
12+4z/6= 12+12 =24 mins
hence he reaches at 5:36

[implex]

will do the others laters
cya

[dashing]

Originally Posted by gautamgomzi

Q. An ant climbing up a vertical pole ascends 12 metre and slips down 5 metre in every alternate hour. If the Pole is 63m high how long will it take to reach the top ?ANS- 16 hr 35 minutes

So ascends 7m in 2 hrs
56m in 16hrs

reamaings --- 63 - 56 = 7

So 12 in 60 min
7 in 7*60/12 = 35 mins

So total 16 hr 35 mins

[monsterkartik]

Originally Posted by dashing

So ascends 7m in 2 hrs
56m in 16hrs

reamaings --- 63 - 56 = 7

So 12 in 60 min
7 in 7*60/12 = 35 mins

So total 16 hr 35 mins

Hey Puys

The thread u guys are using is "The Official CAT 2007 Quant Thread"
One more thread by the name of "The Official CAT 2008 Quant Thread" has been created
would request you to please post all the questions and answers on that thread as it is tuff to keep track of both the threads..
Also would request the MODS to please close this thread

Cheers

Kartik