TCS Questions - 11

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                                        

 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 60^0.                                                                                                                                           

We now know ∟BAD is 30⁰ and ∟EAC is 30^{0                                                                                                                                                                                                                                                                                                                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

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.

                                                                                --- x ---