Wednesday, 2 October 2013

TCS Questions - 13

TCS Questions - 13
1.       The savings of employee equals income minus expenditure. If the income of A,B,C are in the ratio 1:2:3 and their expense ratio 3:2:1 then what is the order of the employees in increasing order of their size of their savings?
Answer: A, B, C
The ratio of income of A, B, and C are 1:2:3. Let us assume their Incomes as 10000, 20000 and 30000
The ratio of their expenditure is 3:2:1. (C spends the least  while A spends the maximum). Assuming the expenditure of A, B and C as 9000, 6000 and 3000, then the
Savings of A, B and C works out to 1000, 14000 and 27000 the ratio being  1:14:27 The increasing order of employees’ savings is A, B and C.

2.       Two full tanks one shaped like the cylinder and the other like a cone contain liquid fuel. The cylindrical tank held 500 litres more than the conical tank. After 200 litres of fuel is pumped out from each tank the cylindrical tank now contains twice the amount of fuel in the conical tank.  How many litres of fuel did the cylindrical tank had when it was full?

Answer: 1200 litres
Let the initial quantity of fuel in the conical tank be ‘x’.  Then the quantity of fuel in the cylindrical tank is (x+500). Now 200 litres of fuel are removed from each tank.
The fuel in the conical tank now is (x-200). The fuel in the cylindrical tank will be
(x+500)-200=(x+300). From the question we know (x+300) = 2*(x-200). Solving this we get the value of ‘x’ as 700 litres. Hence the initial quantity of fuel in the cylindrical tank is (700+500)= 1200 litres.


3.       Eesha bought two varieties of rice costing 50Rs per kg and 60 Rs per kg and mixed them in some ratio. Then she sold that mixture at 70 Rs per kg making a profit of 20 %. What was the ratio of the mixture?

Answer: 1:4
The sale price of Rs 70/kg includes 20% profit. If the profit element is eliminated, we get the sale price as 70 * 100/120 = 58.33. (This can be rounded off to Rs 58.) Now applying Rule of alligation we have
                                                                                          A   50                           60 B
                                                                                                                58 X
                                                                                    (B-X)      2                         8 (X-A)
Thus the ratio of mixture of the two varieties Rs 50 and Rs 60 is 2:8 or 1 : 4.

4.       In a horse racing competition there were 18 horses numbered 1 to 18.The organizers assigned a probability of winning the race to each horse based on horses health and training. The probability that horse one would win is 1/7, that horse two would win is 1/8, and that horse three would win is 1/7. Assuming that tie is impossible, find the chance that one of these three horses would win the race?
Answer: 15/49
The chances of Horse No 1 winning    1/7        Probability of horse No 1 not winning     6/7
The chances of horse No 2 winning     1/8        Probability of horse No 2 not winning    7/8
The chances of horse No 3 winning     1/7        Probability of horse No 3 not winning     6/7.

The chances of any one of these three horses winning the race will be:
(A winning, B and C not winning) + (B winning and C and A not winning) + (C winning and A and B not winning)
Now substituting the relevant information in the above we get the following.
Probability of any one of the three horses winning is arrived at as
(1/7 + 7/8 + 6/7) + ( 1/8 + 6/7 + 6/7) + ( 1/7 + 6/7 + 7/8)   Reducing this we get the value
Of probability of any one of these three horses winning as 15/49.

5.       The missing number in the sequence
5, 6, 15, ?, 89, 170, 291, is

(a) 50                     (b) 40                    (c) 42                     (d) 32

Answer:  (b) 40
6 – 5 = 1  (1^2)       15 – 6 = 9 (3^2)
170 – 89 = 81 (9^2)     291- 170 = 121 (11^2) Going by this we observe that between 89 and 15 we should have two digits namely 5^2 and 7^2. Hence the missing number is
15      5^2 = 40.

6.       Two trains starting at same time, one from Bangalore to Mysore and other in opposite direction arrive at their destination 1 hour and 4 hours respectively after passing each other. How much faster is one train from other?
Answer: One train is four times faster than the other train.

The distances between the two stations remain the same.
The ratio of speeds will be inversely proportional to their respective times.
Let speed of train 1 be S1 and that of train 2 be S2.
Let time taken by train 1 be T1=1hr
and time taken by train 2 be T2=4hr
We now have a ratio

S1:S2 = 1/T1:1/T2 = T2:T1 = 4:1
So train 1 is 4 times faster than train 2.

7.       If f(f(n))+f(n)=2n+3 and f(0)=1, what is the value of f(2012)?
a.2011   b.2012   c.2013   d.4095

Answer: C
                We know f(0) = 1 and f{f(n)} + f(n) = 2n + 3
                Now substituting 0 for n in the above equation, we have f(f(0) + f(0) = 2(0) + 3.
                Since f(0) = 1 substituting this we have f(1) + 1 = 3. Hence f(1) = 2
                Similarly if we put the value of n = 1, then we will get f(2) = 3 and so on .
                The value of f(n) will be n+1
                On this basis f(2012) will be 2013. Hence the answer is ‘c’.

8.       A wooden rod AB is 1 meter long. Raju makes a mark every 3 cm along the rod starting from the end A. Vikram makes a mark every 7 cm and Aditya every 9 cm both starting from the end B. If the rod is cut at each of the points where there is a mark, then how many pieces would it be cut into?

Answer: 51 pieces
Raju will be marking at 33 places starting from the end A. Thus it will give 33 pieces.
Vikram will be marking at 14 places starting from the end B. Of these markings five markings at 93 cm, 72 cm, 51, cm, 30 cm, and 9 cm will coincide with the markings of Raju. Also the marking at 37 cm will coincide with that of Aditya. Thus six markings are common with either Raju or Aditya. Leaving aside this, Vikrams markings will give 8 pieces.
Aditya’s  cutting starting from the end B will give 11 pieces of which the marking at one place 37 cm is common with that of Vikram. Thus the number of pieces will be 10.
Hence the total number of pieces are 33 + 8 + 10 = 51 pieces.

9.       The crew of a rowing team of 8 members is to be chosen from 12 men  (M1, M2, …., M12) and 8 women (W1, W2,…., W8), such that there are two rows, each row occupying one of the 2 sides of the boat and that each side must have 4 members including at least one women. Further it is also known W1 and M7 must be selected for one of its sides while M2, M3 and M10 must be selected for other side. What is the number of ways in which rowing team can be arranged?
Answer:   70 ways.
Side One: Total Number 4.   M2, M3 and M10 are must. This leaves one seat for woman. Out of the eight women, W1 should be on side two. That leaves remaining 7 women from whom one woman can be selected in 7 ways.
Side Two: Total Number 4. W1 and M7 are must. That leaves two remaining seats that can be filled exclusively by either women or one woman and one man. We have 6 remaining women and the two seats can be filled in 6C2 ways ie 15 ways. Suppose we fill one man and one woman this can be done in the following manner. Since there are 6 women and 8 men available the filling can be done in (6C1)*(8C1) = 48 ways.
Thus the remaining seats in the boat can be filled in 7 + 15 + 48 = 70 ways.
10. At the end of 1994, Rohit, was half as old as his grandmother. The sum of the years in which they were born is 3844. How old Rohit was at the end of 1999?
A) 48                                      B) 55                                      C) 49                                      D) 53
Answer: (d)  53 years
Let x and y be the years when the Rohit and grandmother were born.
Thus we have x + y = 3844   …….  (I)
                In 1994 Rohit is half the age of his grandmother. We now have another equation
                (1994 – y) = 2(1994 – x) this will give a value of 2x – y = 1994………..(II)
                Adding (I) and (II) we get 3x = 5838 and x = 1946 Hence Y = 3844 – 1946 = 1898

                In 1994 Rohit’s age was 1994 – 1946 = 48 years.
                In 1994 grand-mother’s age was  1994 – 1898 = 96 years (Twice the age of Rohit)
                So, Rohit’s age in 1999 will be 48 + 5 = 53 years.

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