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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