M4maths Previous Puzzles

04 Mar 2010 Distance from sun rays

Two poles of height 12 m. and 4 m. are situated in such a way that the sun rays through the top of a pole also passes through the top of other. The distance between poles is? (It is given that the sun rays make an angle of 45 degree with the horizon)

OPtion

1) 10
2) 4
3) 6
4) 12
5) 8
6) 9
7) 7
8) 5
9) 3
10)11

Solution

If we make a triangle from top of the pole of height 12 m. upto ground than an other similar triangle
is also obtained from the top of smaller pole. If distance between the poles is x,
then 12/4 = 12/(12-x)
On solving we get x = 8

Option 10)

Correct Option: 5 Best Solution (3)

03 Mar 2010 max area of plot?

If 75 meter wire is used to cover a rectangular plot, then maximum possible area of
the plot covered by this wire is

OPtion

(1) 1406.25
(2) 312.56
(3) 350.2565
(4) 351.5625
(5) 337.5635
(6) 225.3425
(7) 625
(8) 5025.2225
(9) 25.2255
(10) 525

Solution

The rectangle of maximum area is called square.
Hence we should cover a square plot of side 75/4
Area = (75/4)*(75/4) = 351.5625

Correct Option: 4 Best Solution (5)

02 Mar 2010 Wall and Man?

A forms a wall in 10 days and B forms it in 15 days. A and B start the work of forming wall together
but after 2 days A leaves the work. How many days are required for making the remaining wall by B?

OPtion

(1) 6
(2) 9
(3) 8
(4) 10
(5) 12
(6) 15
(7) 16
(8) 20
(9) 5
(10) 4

Solution

One day work of A = 1/10
One day work of B = 1/15
One day work of A and B = 1/10 + 1/15
= 1/6
After 2 days of work remaining work = 1- (2*1/6) = 4/6
No. of days required by B for doing this work = (4/6) / (1/15)
= 10

Correct Option: 4 Best Solution (0)

01 Mar 2010 Happy HOLI

A seller purchases the green colour of HOLI from two dealers, 5 kg. from a dealer at a rate of 60 rupee per kg.
and 7 kg. from other dealer at a rate of 80 rupee per kg.
If he sells the colour after mixing, then its selling rate for getting a profit of 20 % will be

OPtion

(1) 84
(2) 85
(3) 87
(4) 88
(5) 90
(6) 92
(7) 86
(8) 89
(9) 91
(10) 93

Solution

Cost of 5 kg. green colour of HOLI is 60*5 = 300
Cost of 7 kg. green colour of HOLI is 80*7 = 560
Total cost of 12 kg. green colour of HOLI is 300 + 560 = 860
For getting 20 % profit, seller has to receive 860 * 1.2 = 1032 rupee
Hence cost of the colour is 1032/12 = 86

Correct Option: 7 Best Solution (2)

26 Feb 2010 x ?

The sum of a number and its reciprocal is equal to 1/10 multiple of the number of playing card in a deck.
x is?

OPtion

1) 10
2) 6
3) 3
4) 4
5) 5
6) 8
7) 9
8) 7
9) 11
10) 12

Solution

According to the given condition
x + (1/x) = 52/10
or x + (1/x) = 26/5
On solving, we get x = 5, 1/5

Correct Option: 5 Best Solution (5)

25 Feb 2010 How many Monday?

Total number of Mondays in years from 2001 to 2010 are

OPtion

1) 525
2) 523
3) 524
4) 522
5) 526
6) 521
7) 520
8) 519
9) 518
10) 527

Solution

Starting day of the year 2001 is Monday so last day is necessarily Monday, hence total Mondays in the year 2001 are 53
2002 starts from Tuesday, hence total Mondays are 52
2003 starts from Wednesday, hence total Mondays are 52
2004 starts from Thursday, hence total Mondays are 52
Since 2004 is a leap year hence next year starts with a gap of a day
2005 starts from Saturday, hence total Mondays are 52
2006 starts from Sunday, hence total Mondays are 52
2007 starts from Monday, hence total Mondays are 53
2008 starts from Tuesday, hence total Mondays are 52
Since 2008 is a leap year hence next year starts with a gap of a day
2009 starts from Thursday, hence total Mondays are 52
2010 starts from Friday, hence total Mondays are 52

Correct Option: 4 Best Solution (6)

24 Feb 2010 Whistle speed in wind?

Ram hears a sound of whistle after 2 sec. of whistling by Shyam and Shyam hears a sound of whistle
after 3 sec. of whistling by Ram. If Ram and Shyam are in the line of flow of wind,
then velocity of wind in m/s is
(Given that the speed of sound is 300 m/s)

OPtion

(1) 80
(2) 50
(3) 40
(4) 30
(5) 60
(6) 90
(7) Wind is not blowing
(8) Data are insufficient
(9) 70
(10) 20

Solution

Ram hears a sound of whistle after 2 sec. of whistling by Shyam and Shyam hears a sound of whistle after 3 sec.
(greater than 2 sec.) of whistling by Ram. These data indicate that wind is blowing from Shyam to Ram
According to first condition l = (300 + x) 2,
l represents distance between them
According to second condition l = (300 – x) 3
On solving these equations, we get x = 60

Correct Option: 5 Best Solution (4)

23 Feb 2010 Possible solutions ?

If the sum of triple of a number (x) and four times the other is 38, then number of positive integral
solutions for x and y are ?

OPtion

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

Solution

According to given condition 3x + 4y = 38
Hence y = (38 – 3x)/4
Solutions of this equation are (2,8), (6,5), (10,2)

Correct Option: 8 Best Solution (3)

22 Feb 2010 Average of middle number?

The sum of 10 successive numbers is 155, then the average of the number(s) in middle is?

OPtion

1) 15
2) 11.5
3) 16
4) 16.5
5) 15.5
6) 17
7) 18.5
8) 20
9) 10.5
10) 12.5

Solution

We know that the sum of first 10 integer starting from 1 is 55,
On increasing every integer by 10 we can obtain a sum of 155
Middles are 15 and 16, hence average is 15.5

Correct Option: 5 Best Solution (3)

19 Feb 2010 Find the value of X and Y ?

A number (x) is 3 less than the thrice of other number (y) and the sum of their squares is 97.
The values of x and y are respectively?

OPtion

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

Solution

x = 3y – 3 and x2 + y2 = 97
On solving these two equations
x = 9 and y = 4

Correct Option: 4 Best Solution (3)