21) A power unit is there by the bank of a river of 900 meters. A cable is made from power unit to power a plant opposite to that of the river of 2000mts. The cost of the cable below water is Rs. 5/- per meter and cost of cable on the bank is Rs. 4/- per meter. Then find out the amount to be invested to connect those two stations?
Required length of wire = 2000 mts cost of cable below water = 900 * 5 = 4500 cost of cable on the bank of river= (2000 – 900) * 4 = 4400 Total cost = 4500 + 4400 = 8900.
22) A farmer had 20 hens. All but 2 died. How many hens are still alive?
“All but 2” means 2. So, all but 2 died means that there are only two hens are alive and others were dead. So, the answer is 2.
23) At this series: 7, 10, 8, 11, 9, 12… What number should come next?
This is a simple alternating addition and subtraction series. In the first pattern, 3 are added; in the second, 2 are subtracted.
24) A college has 10 basketball players. A 5-member team and a captain will be selected out of these 10 players. How many different selections can be made?
We can select the 5 member team out of the 10 in 10C5 ways = 252 ways. The captain can be selected from amongst the remaining 5 players in 5 ways. Therefore, total ways the selection of 5 players and a captain can be made = 252*5 = 1260.
25) There are 3 gentlemen in a meeting: Mr. Yellow, Mr. Green and Mr. Brown. They are wearing yellow, green and brown ties. Mr. Yellow says: “Did you notice that the colors of our ties are different from our names?” The person who is wearing the green tie says, “Yes, you are right!” Do you know Brown is wearing what colour of tie?
We know that Mr. Yellow was not wearing a yellow tie because of his statement. He also was not wearing the green tie because the one wearing the green tie agreed to his statement. Therefore, Mr. Yellow was wearing a brown tie. Mr. Green was wearing a yellow tie. And Mr. Brown was wearing the green tie.
26) g=1,g=-1,g[n]=2*g[n-1]-3*g[n-2] then calculate g= ?
From the given function g[n] =2*g [n-1]-3*g [n-2] put values of n as first 2 then 3, then 4 and you will get the answer. G = 2*g-3*g=-2-3 =-5 , G=2*g-3*g =2*(-5)-3*(-1)=-7, G  =2*g-3*g=2*(-7)-3*(-5) =1
27) Ten years ago X was half of Y. If the ratio of their present ages is 3:4, what will be the total of their present ages?
Let X’s age 10 years ago = x years. Then, Y’s age 10 years ago = 2x years. (x + 10)/ (2x + 10) = 3/4 => 4 (x + 10) = 3 (2x + 10) x = 5 Total of their present ages = (x + 10 + 2x + 10) = 3x + 20 = 15 + 20 = 35 years.
28) A train can travel 50% faster than a car. Both start from point A at the same time and reach point B 75 kms away from A at the same time. On the way, however, the train lost about 12.5 minutes while stopping at the stations. The speed of the car is:
29) In a circular racetrack of length 100 m, three persons A, B and C start together. A and B start in the same direction at speeds of 10 m/s and 8 m/s respectively. While C runs in the opposite at 15 m/s. When will all the three meet for the first time after the start?
Since the track is a circular track A and B will meet every 50 seconds. i.e. 100 / (10-8). Since it is a multiple of 50 they will be meeting at the starting point every 50 Seconds. If you multiply 15 x 50 you will get 750 and after the second 50 it will be 1500. All of them will meet at the starting point after 100s
30) A class of 100 students. 24 of them are girls and 32 are not. Which base am I using?
Let the base be X. Therefore (X*X + X*0 + 0) = (2*X +4) + (3*X + 2), X * X = 5 * X + 6, X * X – 5 * X -6 = 0, (X- 6) (X+1) = 0 Therefore base is 6.