A man travels
three-fifths of distance AB at a speed of 3a, and the remaining at a
speed of 2b. If he goes from B to A and back at a speed of 5c in the
same time, then:

A....................C...............................B AB = x => AC = 3x/5 and CB = 2x/5. Distance = Speed * Time Time taken to travel the distance between A and C = 3x/5 = 3a * T1 => T1 = x/5a Time taken to travel the distance between C and B = 2x/5 = 2b * T2 => T2 = x/5b Time taken to travel between A and B back and fourth = x= 5c * T => T = x/5c Given that, T = T1 + T2 => x/5a + x/5b = x/5c => 1/a + 1/b = 1/c.

Q. No. :

2

Question :

A can do a piece of
work in 36 days, B in 54 days and C in 72 days. All of them began
together but A left 8 days and B left 12 days before the completion of
the work. How many days in all did C put in till the entire work was finished?

Let work gets completed in x days then A worked for x-8 days then B worked for x-12 days then C worked for x days (x-8)/36+(x-12)/54+x/72=1 x=24

Q. No. :

3

Question :

A person travels
through 5 cities - A, B, C, D, E. Cities E is 2 km west of D. D is 3 km
north-east of A. C is 5km north of B and 4 km west of A. If this person
visits these cities in the sequence B - C - A - E - D, what is the
effective distance between cities B and D?

A :

13 km

B :

9 km

C :

10 km

D :

11 km

Answer: A

Q. No. :

4

Question :

In a watch, the
minute hand crosses the hour hand for the third time exactly after every
3 hrs 18 min 15 seconds of watch time. What is the time gained or lost
by this watch in one day?

In a correctly running watch, the crossing of hands should take place exactly after every (720/11) minutes. In this watch it takes after (3 hrs 18 min 15 seconds)/3 = 1 hour 6 min 5 sec = 66 (5/60) minutes of watch time. so, this watch loses time = 720/11 - [66 (5/60)] => 83/132 minutes in (720/11) minutes. so, in 1 day i.e 24* 60 minutes it will lose 83/6 minutes i.e. 13 min 50 second.

Q. No. :

5

Question :

A cube of side 12
cm is painted red on all the faces and then cut into smaller cubes, each
of side 3 cm. What is the total number of smaller cubes having none of
their faces painted?

A :

16

B :

8

C :

12

D :

24

Answer: B

Q. No. :

6

Question :

A, B and C can do a
work in 5 days, 10 days and 15 days respectively. They started together
to do the work but after 2 days A and B left. C did the remaining work
(in days)

A :

1

B :

3

C :

4

D :

5

Answer: C

Q. No. :

7

Question :

A student gets an
aggregate of 60% marks in five subjects in the ratio 10 : 9 : 8 : 7 : 6.
If the passing marks are 50% of the maximum marks and each subjects has
the same maximum marks, in how many subjects did he pass the exam?

Take the maximum marks in each subject is 100. So qualifying mark is 50. On a total that fellow gets 60 x 5= 300. We can write (10+9+8+7+6)a=300 => a=15/2 In 5 subjects he gets 75,67.5,60,52.5,45. He passes in 4 subjects.

Q. No. :

8

Question :

Two trains, 200 and
160 meters long take a minute to cross each other while traveling in
the same direction and take only 10 seconds when they cross in opposite
directions. What are the speeds at which the trains are traveling?

When the trains are moving in same direction (200+160)=(V1-V2)*60 When the trains are moving in opposite direction (200+160)=(v1+v2)*10 Equating we get v1=21m/s and v2=15m/s

Q. No. :

9

Question :

The horizontal
distance of a kite from the boy flying it is 30 m and 50 m of cord is
out from the roll. If the wind moves the kite horizontally at the rate
of 5 km per hour directly away from the boy, how fast is the cord being
released?

Method 1: z^{2} = x^{2} + y^{2} z = √x^{2} + y^{2} dz/dt = 2x/(2√x^{2} + y^{2}) dx/dt as y is constant Initially x = 30m, y = 40m, dx/dt = 5km/hr dz/dt_{initial} = 2 * 30/(2*50) * 5 = 3 kmph

Method 2: Initial position of kite: x= 30 y= 40 z= 50

After 1hr, wind made the kite move 5km directly away from the boy, so, position of kite after 1 second: x= 30 + 1.39=31.39(because of wind, 5kmph = 1.39m/s) y= 40 z= √( 31.39*31.39+40*40) = 50.846

Now in 1sec, cord has moved 0.846m => 3kmph So, cord is released at the rate of 3kmph.

Q. No. :

10

Question :

After a discount of
11.11%, a trader still makes a gain of 14.28%. At how many percent
above the cost price does he mark his goods?

A :

28.56 %

B :

35%

C :

22.22 %

D :

None of these

Answer: A

Q. No. :

11

Question :

I bought 5 pens, 7
pencils and 4 erasers. Rajan bought 6 pens, 8 erasers and 14 pencils for
an amount which was half more than what I had paid. What percent of the
total amount paid by me was paid for the pens?

Suppose cost of pen pencil and eraser is x y and z respectively. According to question, 6x+8z+14y = 3/2(5x+7y+4z) or 3x = 7y + 4z

Now percent of the
total amount paid for the pens = 5x/(5x+7y+4z)*100 =5x/(5x+3x)*100 = 62.5 %

Q. No. :

12

Question :

A man has nine
friends, four boys and five girls. In how many ways can he invite them,
if there have to be exactly three girls in the invitees?

A :

320

B :

160

C :

80

D :

200

Answer: B

Q. No. :

13

Question :

A can complete a
project in 20 days and B can complete the same project in 30 days. If A
and B start working on the project together and A quits 10 days before
the project is completed, in how many days will the project be
completed?

New revenue = 1.04xy Old revenue xy Percentage Increase 4% Ans

Q. No. :

15

Question :

The average marks
of a student in ten papers are 80. If the highest and the lowest scores
are not considered, the average is 81. If his highest score is 92, find
the lowest.

A :

55

B :

58

C :

60

D :

62

Answer: C

Q. No. :

16

Question :

Two liquids A and B
are in the ratio 5 : 1 in container 1 and in container 2, they are in
the ratio 1 : 3. In what ratio should the contents of the two containers
be mixed so as to obtain a mixture of A and B in the ratio 1 : 1?

In 1 lit Container 1 contains 5/6 lit A and 1/6 lit B In 1 lit Container 2 contains 1/4 lit A and 3/4 lit B Suppose x lit of 1 and y lit of 2 are mixed. So in the mixture A= 5/6x + 1/4y B = 1/6x + 3/4y

According to question, 5/6x+1/4y = 1/6x + 3/4y or x:y = 3:4

Q. No. :

17

Question :

If a number 774958A96B is to be divisible by 8 and 9, the values of A and B, respectively, will be:

If the digit is divisible by 8 then, its last three number should be divisible by 8... So, possibility of B's value is either 0 or 8. It's divisible by 9 if the sum of the digits is : A+55+B if B=0 : A+55 should be divisible by 9 : A=8 (or A+55 -> A+5+5->A+10->A+1) if B=8, A+9 should be divisible by 9, A=0 Possible values of A, B are (8,0) and (0,8).

Q. No. :

18

Question :

If log 2 = 0. 3010, then find how many digits are contained in the number 2^{56}

The sum of the
areas of two circles which touch each other externally is 153π. If the
sum of their radii is 15, find the ratio of the larger to the smaller
radius.

A closed wooden box
of thickness 0.5 cm and length 21 cm, width 11 cm, and height 6 cm, is
panted on the inside. The cost of painting is Rs 70. What is the rate
of painting in rupees per sq. cm?