Aptitude Question Bank For AIEEE SSC

A man is 24 years older than his son. In two years, his age will be twice the age of his son. The present age of his son is: A. 14 years B. 18 years C. 20 years D. 22 years Answer:  Option  D Explanation: Let the son's present age be  x  years. Then, man's present age = ( x  + 24) years.  ( x  + 24) + 2 = 2( x  + 2)   x  + 26 = 2 x  + 4   x  = 22.

  A father said to his son, "I was as old as you are at the present at the time of your birth". If the father's age is 38 years now, the son's age five years back was: A. 14 years B. 19 years C. 33 years D. 38 years Answer:  Option  A Explanation: Let the son's present age be  x  years. Then, (38 -  x ) =  x  2 x  = 38.   x  = 19.  Son's age 5 years back (19 - 5) = 14 years.

The sum of ages of 5 children born at the intervals of 3 years each is 50 years. What is the age of the youngest child? A. 4 years B. 8 years C. 10 years D. None of these Answer:  Option  A Explanation: Let the ages of children be  x , ( x  + 3), ( x  + 6), ( x  + 9) and ( x  + 12) years. Then,  x  + ( x  + 3) + ( x  + 6) + ( x  + 9) + ( x  + 12) = 50  5 x  = 20   x  = 4.  Age of the youngest child =  x  = 4 years.

Father is aged three times more than his son Ronit. After 8 years, he would be two and a half times of Ronit's age. After further 8 years, how many times would he be of Ronit's age? A. 2 times B. 2  1 times 2 C. 2  3 times 4 D. 3 times Answer:  Option  A Explanation: Let Ronit's present age be  x  years. Then, father's present age =( x  + 3 x ) years = 4 x  years. (4 x  + 8) = 5 ( x  + 8) 2  8 x  + 16 = 5 x  + 40  3 x  = 24   x  = 8. Hence, required ratio = (4 x  + 16) = 48 = 2

Two, trains, one from Howrah to Patna and the other from Patna to Howrah, start simultaneously. After they meet, the trains reach their destinations after 9 hours and 16 hours respectively. The ratio of their speeds is: A. 2 : 3 B. 4 : 3 C. 6 : 7 D. 9 : 16 Answer:  Option  B Explanation: Let us name the trains as A and B. Then, (A's speed) : (B's speed) =  b  :  a  =  16  :  9  = 4 : 3.

Two trains of equal lengths take 10 seconds and 15 seconds respectively to cross a telegraph post. If the length of each train be 120 metres, in what time (in seconds) will they cross each other travelling in opposite direction? A. 10 B. 12 C. 15 D. 20 Answer:  Option  B Explanation: Speed of the first train = 120 m/sec = 12 m/sec. 10 Speed of the second train = 120 m/sec = 8 m/sec. 15 Relative speed = (12 + 8) = 20 m/sec.  Required time = (120 + 120) sec = 12 sec. 20

Two goods train each 500 m long, are running in opposite directions on parallel tracks. Their speeds are 45 km/hr and 30 km/hr respectively. Find the time taken by the slower train to pass the driver of the faster one. A. 12 sec B. 24 sec C. 48 sec D. 60 sec Answer:  Option  B Explanation: Relative speed = = (45 + 30) km/hr = 75 x 5 m/sec 18 = 125 m/sec. 6 We have to find the time taken by the slower train to pass the DRIVER of the faster train and not the complete train. So, distance covered = Length of the slower train. Therefore, Distance covered = 500 m.  Required time = 500 x 6 = 24 sec. 125

How many seconds will a 500 metre long train take to cross a man walking with a speed of 3 km/hr in the direction of the moving train if the speed of the train is 63 km/hr? A. 25 B. 30  C. 40 D. 45 Answer:  Option  B Explanation: Speed of the train relative to man = (63 - 3) km/hr = 60 km/hr = 60 x 5 m/sec 18 = 50 m/sec. 3  Time taken to pass the man = 500 x 3 sec 50 = 30 sec.

Two trains running in opposite directions cross a man standing on the platform in 27 seconds and 17 seconds respectively and they cross each other in 23 seconds. The ratio of their speeds is: A. 1 : 3 B. 3 : 2 C. 3 : 4 D. None of these Answer:  Option  B Explanation: Let the speeds of the two trains be  x  m/sec and y m/sec respectively. Then, length of the first train = 27 x  metres, and length of the second train = 17 y  metres. 27 x  + 17 y = 23 x +  y  27 x  + 17 y  = 23 x  + 23 y  4 x  = 6 y x = 3 . y 2

The length of the bridge, which a train 130 metres long and travelling at 45 km/hr can cross in 30 seconds, is: A. 200 m B. 225 m C. 245 m D. 250 m Answer:  Option  C Explanation: Speed = 45 x 5 m/sec = 25 m/sec. 18 2 Time = 30 sec. Let the length of bridge be  x  metres. Then, 130 +  x = 25 30 2  2(130 +  x ) = 750   x  = 245 m.

A can do a work in 15 days and B in 20 days. If they work on it together for 4 days, then the fraction of the work that is left is : A. 1 4 B. 1 10 C. 7 15 D. 8 15 Answer:  Option  D Explanation: A's 1 day's work = 1 ; 15 B's 1 day's work = 1 ; 20 (A + B)'s 1 day's work = 1 + 1 = 7 . 15 20 60 (A + B)'s 4 day's work = 7 x 4 = 7 . 60 15 Therefore, Remaining work = 1 - 7 = 8 . 15 15