M4maths Previous Puzzles

27 May 2010 2mm drop of water?

A tank contains 1 litre of water. Water is falling drop wise from the tank. Radius of the drop is 2 mm.
If every drop takes 1 sec. to fall from the tank, then the total time required to make the tank empty is

OPtion

1) 8h 16m 25s
2) 8h 17m 37s
3) 8h 15m 23s
4) 8h 10m 21s
5) 8h 3m 24s
6) 8h 13m 35s
7) 8h 11m 28s
8) 8h 22m 56s
9) 8h 19m 34s
10) 8h 23m 23s

Solution

Total amount of water = 1 litre = 1000000 cubic mm
Volume of 1 drop of water = 4*π*r*r*r/3 = 4*π*2*2*2/3 cubic mm and this drop takes 1 sec to fall from the tank
Hence total time taken = 1000000/(32*π/3) sec.
= 29856.688 sec.
= 29856.688/3600 hours
= 8.2935244 h
= 8h 17m 37s

Correct Option: 2 Best Solution (4)

26 May 2010 Unit place?

Digit in the unit place of 14^14 is

OPtion

1) 6
2) 7
3) 8
4) 9
5) 1
6) 2
7) 3
8) 4
9) 5
10) 0

Solution

14^14 = (14*14)7 = 196*196*.......7 times = a number with unit place 6

Correct Option: 1 Best Solution (4)

25 May 2010 Mixture Of 3 component

A mixture contains 3 components A, B and C in the ratio 3:4:5. If difference of the amount of B and C is 19 Kg,
then total mass of the mixture is

OPtion

1) 189
2) 230
3) 224
4) 220
5) 210
6) 228
7) 168
8) 320
9) 290
10) 300

Solution

Let the amounts of A, B and C are 3x, 4x and 5x respectively, then according to the given condition 5x – 4x = 19

Hence x = 19

Total amount of the mixture = 12 x = 12*19 = 228

Correct Option: 6 Best Solution (18)

24 May 2010 Find the number

A number is such that square of its successor is successor of its 7 multiple. The number is?

OPtion

1) 8
2) 6
3) 7
4) 5
5) 9
6) 1
7) 2
8) 3
9) 4
10) 10

Solution

According to given condition (x+1)2 = 7x +1

On solving this equation, we get x = 5

Correct Option: 4 Best Solution (10)

21 May 2010 Drop four Letters

There are four different letters and four different letter boxes, in how many methods these letters can be dropped in the boxes,
if all the four letters in a single box are not allowed:

OPtion

1) 250
2) 248
3) 256
4) 320
5) 252
6) 128
7) 224
8) 90
9) 4
10) 16

Solution

Total no. of methods without any condition = 4*4*4*4 = 256
No of methods of taking all the four letters in a box = 4
Hence required methods with given condition = 256-4 = 252

Correct Option: 5 Best Solution (4)

20 May 2010 Investment?

A man invests a sum in two parts in two different businesses. In first business, he gets a profit of 16 %,
whereas in second business, he losses 16 %. If his total investment and overall profit are 39000 and 1760 rupee
respectively then the investment in second business is

OPtion

1) 12000
2) 15000
3) 16000
4) 18000
5) 20000
6) 21000
7) 24000
8) 25000
9) 14000
10) 10000

Solution

Let the investment in second business is x rupee and that in the first business is (39000-x).
According to given condition
(39000 - x)*0.16 - x*0.16 = 1760
or 39000 - x - x = 1760/0.16
or 39000 – 2x = 11000
or x = 14000

Correct Option: 9 Best Solution (9)

19 May 2010 Arrange boy and girl

How many ways are possible to arrange 4 boys and 3 girls for a dinner, if there are two straight benches
of capacity 5 and 2 persons for their sitting?

OPtion

1) 720
2) 5040
3) 2520
4) 840
5) 4320
6) 2460
7) 2860
8) 120
9) 24
10) 1

Solution

Total no. of persons = 7
Since benches are straight, therefore arranging them in benches of capacity 5 and 2 persons is
equivalent to arranging them in a straight bench of capacity 7 persons.
Total no. of methods = 7*6*5*4*3*2*1 = 5040

Correct Option: 2 Best Solution (9)

18 May 2010 Placement between tow station

The displacement between Ram Nagar and Shyam Nagar is 20 km. and that between Shyam Nagar and Gandhi Nagar is 20 km.
The possible displacement range between Ram Nagar and Gandhi Nagar is

OPtion

1) (0 km., 40 km.]
2) (20 km., 40 km.]
3) (10 km., 40 km.]
4) (30 km., 40 km.]
5) (0 km., 30 km.]
6) (0 km., 20 km.]
7) (0 km., 50 km.]
8) (35 km., 40 km.]
9) (20 km., 30 km.]
10) (40 km., 50 km.]

Solution

You can draw a diagram for this arrangement.

Correct Option: 1 Best Solution (12)

17 May 2010 Find the value of x

If x + x^2 + x^3 + x^4 + x^5 + x^6 +.......... Upto ∞(infinite) = 1
Then x is equal to

OPtion

1) 2/3
2) 1/3
3) 1/4
4) 1/2
5) 4/5
6) 8/9
7) 1/5
8) 3/5
9) 2/9
10) 7/8

Solution

x + x^2 + x^3 + x^4 + x^5 + x^6 +........ Upto ∞ = 1
x (1 + x + x^2 + x^3 + x^4 + x^5 + x^6 +........ Upto ∞) = 1
x [1 + (x + x^2 + x^3 + x^4 + x^5 + x^6 +........ Upto ∞)] = 1
x [1 + 1] = 1
x = 1/2

Correct Option: 4 Best Solution (19)

14 May 2010 Water Density?

In a bucket of 15 litre volume water is filled completely and its density is 1000 gm/litre.
What will be the density (gm/litre) of water filled in a bucket of volume 30 litres?

OPtion

1) 900
2) 1200
3) 1500
4) 1800
5) 2000
6) 2100
7) 2400
8) 1000
9) 800
10) 875

Solution

Density is a fixed term and does not depend upon volume.

Correct Option: 8 Best Solution (8)