Sunday, 9 February 2014

TCS - Recent Questions - 1

TCS – Recent Questions - 1

1.       An empty tank is filled with an inlet pipe ‘A’ in 42 minutes. After 12 minutes an outlet pipe ‘B’ is opened which can empty the tank in 30 minutes. After 6 minutes another inlet pipe ‘C’ opened into the same tank, which can fill the tank in 35 minutes and the tank is filled. Find the time taken to fill the tank?
Ans: 45 minutes.

Pipe A in one minute fills 1/42 of the tank. Pipe A is totally kept open for 12 + 6 -> 18 minutes before Pipe C is opened. Thus in 18 minutes Pipe A fills 18/42 -> 3/7 capacity of the tank.
Pipe B can drain the tank in 30 minutes and in one minute can drain 1/30 of the tank.
Pipe B is kept open for 6 minutes before Pipe C is opened. In this 6 minutes it would have drained 6/30 -> 1/5 capacity of the tank.
Hence, after 18 minutes the tank is filled up to - >  3/7 – 1/5 -> 8/35 capacity.
The remaining capacity to be filled is -> 27/35
All the three pipes are now running to fill this quantity.
Pipe C in one minute can fill 1/35 capacity.
Now in one minute both Pipes A and C fills and C drains. The quantum filled in one
Minute is ->  1/42 + 1/35 – 1/30 -> 2/70.
Thus to fill the remaining capacity of 27/35 the time taken will be 27/35 * 70/2 -> 27 minutes.
Hence, the total time taken to fill the tank is 12 + 6 + 27 = 45 minutes.

2.       Mr and Mrs smith had invited 9 of their friend and their spouses for party at wiki
Beach resort. They stand for a group photograph. If Mr Smith never stands next to Mrs Smith then in how many ways the group can be arranged to stand in the row?

(a) 20!             (b) 19!+18!                  (c) 18*19!        (d) 2*19!
                Ans: (c)

The invited friends including their spouses totals 18 and with either Mr Smith or Mrs Smith it comes to 19. These 19 members can be arranged in a row in 19! Ways.
Now there are 20 places available for one of the Smith’s to stand. But, Mr and Mrs Smith o not stand together in the photograph. This practically eliminates 2 places in the row and the remaining Smith can be accommodated in the remaining places in 18 ways.
Thus the answer is 18 * 19!

3.       Tim and Elan are 90 km from each other, and they start to move towards each other simultaneously. Tim walks at speed of 10 kmph and Elan at 5kmph. After every hour they double their speed. What is the distance that Tim will cover before he meets Elan?

(a) 45                     (b) 60                    (c) 20                     (d) 80
                Ans: (b)
After one hour the distance between Tim and Elan will be 75 km. After 2 hours the distance gets reduced to 45 km. During the third hour Tim speed is 40kmph and Elan’s speed 20 kmph. The ratio of their speed now is 2 : 1.
Thus when Tim covers 30 km Elan would have covered 15 km and both will meet.
Hence the distance travelled by Tim is 10 + 20 + 30 -> 60 km.
 
4.       A Grocer bought 24 kg coffee beans at price X per kg. After a while one third of stock got spoiled and he sold the rest for $200 per kg and made a total profit of twice the cost. What must be the price of X?

(a)    $33 1/3         (b)  $66 2/3         (c)  $44 4/9          (d)  $50 1/3
Ans: (b)

The purchase cost for 24 kg coffee is 24X.
One third of the stock got spoiled. So the remaining stock is 16 kg. This was sold at $200 per kg. Thus the sales realisation is 16 * 200 -> $3200. This is equivalent to twice the purchase cost.  Hence we have 2*24X = $3200. Solving we get the value of X as $66 2/3.

        5. How many kgs of rice costing Rs. 8 per kg must be mixed with 86 kg of rice costing Rs.
5.00 per kg so that 20% gain may be obtained by selling the mixture at Rs. 7.20 per kg?
Ans: 43 kg.

The selling price of Rs 7.20 includes 20% profit. Hence, the cost price of the mixture is Rs 6.00.  Applying the rule of alligation we get the ratio of mixtures between the cheaper and costlier varieties as 2 : 1. Since the cheaper quantity is 86 kg the costlier variety should be 43 kg in the mixture.

6.       The diagonal of a square is twice the side of an equilateral triangle. The ratio of Area of the triangle to the Area of square is?
(a)    √3:8                               (b)  2:5                  (c)  3:6                   (d)  2:4
Ans: (a)

Let ‘a’ be the side of the equilateral triangle. Then the diagonal of the square is ‘2a’.
Area of the triangle = √3/4 a2.  The area of the square is = ½ d2 where ‘d’ is the diameter -> 2a -> 4a2/2  Solving we get the ratio as √3 : 8

7.       Raj tossed 3 dices and the results are noted down. Then what is the probability that raj gets
a sum of 10?
(a)    1/72                               (b)   1/9                                (c)  25/216           (d)   1/8
Ans: (d)
               
The possibility of Raj getting 10 is in the following manner: 136/145/154/163., 226/235/244/253/262; 316/325/334/343/352/361; 415/424/433/442/451/; 514/523/532/541/; 613/622/631/
27 possible manner as against total possibilities of 216 (6 x 6 x 6) ie 27/216 or 1/8

8.       Length of minute hand is 5.4 cm. What is the area covered by this in 10 minutes?
(a)    50.97                             (b)  57.23             (c)  55.45              (d)     59.14
Ans: NONE

The minute hand would have covered 600 in 10 minutes and the area of the arc formed by this movement is given by pi * r2 * Ɵ/360 where Ɵ is the angle of the arc. The length of the minute hand is the radius as the hand goes around the clock. Applying these information we
Will get the area covered by the minute hand in 10 minutes as 15.27 sq.cm.

9.      There are three buckets of capacity 8, 5 and 3 litres. Of these the 8 litre bucket is fully filled. How would you fill exactly 4 litres in each of the 8 litre and 5 litre buckets in minimum number of operations?
Ans: 7

                                                Remaining Qty:         8 LTR     5LTR       3 LTR
Step 1 ->  Pour from 8 litre to 5 litre full.                       3            5              0
Step 2 ->  Pour from 5 litre to 3 litre full                        3            2              3
Step 3 ->  Pour full 3 litres to 8 litre                              6            2              0
Step 4 ->  Pour the 2 litre from 5 litres to 3 litre             6            0              2
Step 5 ->  Pour from 8 litres to 5 litre full                       1            5              2
Step 6 ->  Pour from 5 litre to 3 litre full                         1           4              3
Step 7 ->  Pour the full 3 litres into 8 litre                       4           4              0

10.   n! has 13 zeroes. Than what is the highest and lowest value of n?
Ans: 59! And 55!

The number of zeroes in any factorial is given by the equation -> n/5 + n/52








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