TCS Questions - 11
1.
From the top of a 9 mtr high
building AB, the angle of elevation to the top of a tower CD is 300
and the angle of depression of the foot of the tower is 600. What is
the height of the tower? C
From the top of a 9 mtr high
building AB, the angle of elevation to the top of a tower CD is 300
and the angle of depression of the foot of the tower is 600. What is
the height of the tower? C 
A:
12, B:
18 C: 9
D: 15 
Answer: B
Angle of elevation from A to C is 300 and
angle of depression E A
from A to D is 600.
We now know ∟BAD is 300 and ∟EAC
is 300 9
mtrs
Let the distance BD be x. Then the distance
EA also is x D B
Let EC be Y
Tan BAD
= BD/BA = x/9 = √3. Hence x = 9√3
Tan EAC
= EC/ EA = Y/9√3 = 1/√3 Hence Y =
9
AB = 9 mtrs = ED. Hence the height of CD the tower is 9 + 9 = 18 mtrs.
2.
In a mixture of A, B, and C if A and B are mixed
in the ratio 3:5 and B and C are mixed in the ratio 8:5 and if the final
mixture is 35 ltrs, then what is the quantity of B?
A: 13.34 B:
15.73 C: 16.73
D: 9.45
Answer:
B
We have two different values for B in the
above ratio.
A : B :: 3 :5 and B : C :: 8 : 5 We shall now make the value of B the same in
both the ratios.
Multiplying A : B by 8 and B : C by 5 we
get new ratios where the value of B is the same.
A : B :: 24 : 40 and B : C :: 40 : 25
Combining all the three we have the ratio A
:B : C :: 24 : 40 : 25 The total
quantity of the final mixture is 35 ltrs.
Quantity
of B in the mixture is (35 x 40) / 89 =
15.73
3.
My flight takes off at 2.00 A.M. from a place
18N 10E and after 10 hours flight lands at a place with coordinates 36N 70W.
What is the local time when the plane lands at the destination?
A:
12 noon B: 6.40 a.m. C:
5.20 p.m. D: 6.50 a.m.
Answer:
B
The longitudinal difference between the two
stations is 70W + 10E = 800
For every one degree variance in the
longitude the time difference is 4 mts. As you go towards East the time
increases, and as you go west the time decreases. In this case the flight is
towards west and the destination time will be less than the originating
station.
The time variance between the two stations
is 4 x 80 = 320 minutes or 5 hours and 20 minutes.
The flying time was 10 hours. The time of
departure was 2.00 a.m. Hence after 10 hours the time at the originating
station was 12.00 noon. ( 2 + 10 ). The
time difference between the two stations is 5 hrs 20 mts. Hence the time of
landing at the destination was
12.00
– 5.20 = 6.40 a.m.
4.
In a100 mtrs race, A beats B by 15 mtrs and B
defeats C by 10 mtrs. If A beats C by 5 seconds then find the speed of C.
A: 5
mtrs/sec B: 4.7 mtrs/sec C: 4 mtrs/sec D:
4.5 mtrs/Sec
Answer:
B
When A covers 100 meters, B was at a distance
of 85 meters. When B covers 100 meters C was at a distance of 90 meters.
Now, When A covers 100 meters C was at a
distance equal to (85 x 90)/100 = 76.50 meters.
A defeats C by 5 seconds. In other words to
run 100 – 76.50 = 23.50 meters C takes 5 seconds. Hence the speed of C = 23.50/5 = 4.70meters per sec.
5.
Oshkosh used a study of colours in African
National Flags. He found 38 flags have
Red, 20 have Blue and 13 have both Red and Blue and 8 have neither Red nor
Blue. How many flags have:
a)
Have Red but not Blue?
b)
Have Blue but not Red?
c)
Were included in the study?
A: 25, 7, 53 B:
38, 20, 79 C: 25, 7, 66 D:
30, 20, 60
Answer: A
38 flags have Red less 13
flags having Red and Blue. Hence flags having only Red are 25
20
flags have Blue less 13 flags having Red and Blue. Hence flags having only Blue are 7
Total number of flags
studied: Only Red 25. Only Blue 7. Both
Red and Blue 13. Neither Red nor Blue 8. Total
flags 25+7+13+8 = 53.
6.
How
much per cent must be added to the cost price of goods so that a profit of 20%
must be made after giving a discount of 10% from the market price.
A) 204
B) 30
C) 33 3/3
D) 25
E) 10
A) 204
B) 30
C) 33 3/3
D) 25
E) 10
Answer : C
This
question can be answered from the choices given. The marked price will be
133.33% .10% discount on this will be 13.33%. Reducing this we get the sale price
as 120% which gives 20% profit.
7.
In
a class of boys and girls Vikas's rank is 9th and Tanvi's Rank is 17th .
Vikas's Rank among the boys in that class is 4th from the top and 18th from the
bottom and Tanvi's rank among the girls is 8th from top and 21st from bottom.
In the order of rank, how many girls are there between Tanvi and Vikas ?
Answer: 2 Girls.
Vikas Tanvi
Vikas rank 9
17
Vikas rank among the boys
4 (from top) Tanvi’s rank
among the Girls 8 (from top)
Vikas rank among boys 18 (from last) Tanvi’s rank among the
girls 21(from last)
Total number of Boys (4+18-1) 21
Total number of Girls (8+21-1) 28
Total Students in the class 21 + 28 = 49
There are 5 Girls and 3 boys above
Vikas rank which is 9.
There are 7 Girls and 9 boys above
Tanvis rank which is 17. Hence the
number of Girls between Vikas and Tanvi are 2
8.
Two
men together start a journey in the same direction. They Travel 9km/hr and
15km/hr respectively. After travelling for 6 hours the man travelling at 9km/hr
doubles his speed and both of them finish the distance in the same time. How
many hours will they take to reach their destination?
Answer: 18 hours.
Let
the two men be A and B. A travels at 9kmph and B travels at 15kmph.
After
6 hours A would have covered 9 x 6 = 54
kms
After
6 hours B would have covered 15 x 6 = 90
kms. B is ahead of A by 36 kms.
A
now increases his speed to 18kmph and B continues at 15 kmph. The relative
speed between A and B now is 18 – 15 = 3kmph. To cover the difference in distance
of 36 kms A would take 36/3 = 12 hours.
Thus A would take totally 18 hours to cover
a distance of 270kms. (6*9 + 12*18)
B also would take 18 hours to cover the
distance of 270 kms ( 15*18).
9.
A
train covers a distance between stations A and B in 45 Minutes. If the speed is
reduced by 5km/hour. It will cover the same distance in 48 Minutes, What is the
distance between station A & B in kms?
Answer: 60 km
Speed
* time would give the distance. Let the
initial speed be x kmph. The time taken is 45 minutes or ¾ hrs.
Hence
Distance = 3x/4. Now the speed is
reduced by 5 kms and the time taken is 48 minutes or 4/5 hrs.
Hence
Distance = (x-5)*4/5 . Both these are equal. So we have an eqution
3x/4
= (4x-20)/5. Solving we get the value
of x as 80kmph. At 80 kmph the time taken to cover the distance
Was
¾ hours. Hence the distance between A
and B = 80 * ¾ = 60 km.
10.
The
average set of numbers is 46, if 4 numbers whose average is 52 are subtracted
from this set , the
average
becomes 44.5...find the original number of numbers in the set ?..
Answer:
20.
Let the set of numbers be X. Then the total
of the numbers are 46 * X = 46X.
4 numbers with average of 52 are removed.
Total of these 4 numbers is 4*52 = 208.
The new average for (X-4) numbers is 44.5.
Thus we have an equation
46X = 44.5(X-4) + 208. Solving
we get the value for X as 20.
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