M4maths Previous Puzzles

13 Sep 2017 Distance

Two ships are sailing in the sea on the two sides of a lighthouse. The angle of elevation of the top of the lighthouse is observed from the ships are 30° and 45° respectively. If the lighthouse is 169 m high, the distance between the two ships is:

OPtion

1) 460.72 m
2) 468.72 m
3) 463.72 m
4) 464.72 m
5) 461.72 m
6) 465.72 m
7) 467.72 m
8) 469.72 m
9) 462.72 m
10)None of these

Solution

Let AB be the lighthouse where A is the bottom point of light house and C and D be the positions of the ships.
Then, AB = 169 m, Angle ACB = 30° and angle ADB = 45°.
AB/AC = tan 30° = 1/sq root(3)
=> AC = AB * sq root(3) = 169*3^(1/2)

AB/AD = tan 45° = 1
=> AD = AB = 169

CD = (AC + AD) = 169(3^(1/2) +1)
= 461.72

Correct Option: 5 Best Solution (7)

12 Sep 2017 Speed and Time

A boatman goes 3 km against the current of the stream in 2 hour and goes 1.5 kms along the current in 30 minutes. How long will it take to go 12 km in stationary water?

OPtion

1) 5 hours 33 minutes
2) 5.23 hours
3) 5 hours 30 minutes
4) 5.13 hours
5) 5 hours 15 minutes
6) 5.03 hours
7) 5 hours 20 minutes
8) 5 hours 25 minutes
9) 5.5 hours
10)None of these

Solution

Speed (upstream) =3/2 = 1.5 km/hr
Speed (downstream)=1.5/0.5= 3 km/hr

Speed in still water = 1/2 (1.5+3) = 2.25 km/hr

Time taken in stationary water to go 12 KM = 12/2.25 = 5.33 hr = 5 hours 20 minutes

Option 7)

Correct Option: 7 Best Solution (11)

11 Sep 2017 Age

A father said to his son, "I was as old as you are at the present at the time of your birth". If the father's age is
74 years now, what would be the son's age after thirteen years?

OPtion

1) 20
2) 21
3) 23
4) 24
5) 37
6) 24
7) 40
8) 44
9) 47
10) None of these

Solution

Let the sons current age be x
So fathers age x years back when son was born => 74-x = x
Solving we get x = 37
13 Years later son's age = 37+13 = 50 years

Correct Option: 10 Best Solution (39)

08 Sep 2017 Trains

Two trains each 350 meter long, are running in same directions on parallel tracks. If their speeds are 46 km/hr and 60 km/hr respectively, the time taken by the slower train to pass the driver of the faster one is?

OPtion

1) 75 seconds
2) 91 seconds
3) 89 seconds
4) 90 seconds
5) 80 seconds
6) 95 seconds
7) 100 seconds
8) 85 seconds
9) 88 seconds
10) None of these

Solution

Relative speed= 60-46 = 14 km/hr = 14 * 5/18 = 35/9 m/sec

We are calculating the time taken by the slower train to pass the driver of the faster one.
Hence, distance = length of the slower train = 350 meter

Time = 350/35/9 = 90 seconds

Option 4)

Correct Option: 4 Best Solution (15)

07 Sep 2017 Probability

With Dhoni and Bhuvi at the crease Cricket Team of India needs to score 9 runs in last 2 balls to win the match. What is the probability that India doesn't lose the match? Assume that:
-There were no wide balls or no balls bowled in these 2 balls.

-No Wicket has fallen in these 2 balls

-No Overthrows or extra runs were scored in these 2 balls

-In case if run(s) are scored on any of these 2 balls it can only be one of these values: 1, 2, 3, 4 & 6

This also implies that it’s quite possible that zero runs are scored on a particular ball

OPtion

1) 1
2) 9/36
3) 11/36
4) 10/35
5) 5/19
6) 2/9
7) 5/36
8) 5/18
9) 7/36
10) None of these

Solution

On any of these 2 balls the possible runs which can be scored are: 0,1,2,3,4,6
India will lose the match if it score 7 or less - 8 would be a tie which implies that India didn't lose the match and 9 or above means India won

So possible pair of runs in 2 balls which will result in India not losing (i.e. winning or tie) :
(6,2), (6,3), (4,4), (6,4), (2,6), (3,6), (4,6), (6,6) => count of pairs = 8

Probability that India will not lose = 8/36 = 2/9

Correct Option: 6 Best Solution (5)

06 Sep 2017 Radius and Volume

3 solid spheres of radius 2 m, 1 solid cylinder of radius 3 m, height 4 meter and 2 solid cones of radius 4 m, height 3 m are melted to form a bigger solid sphere. What is the radius of this bigger solid sphere in meters?

OPtion

1) 4.22
2) 4.14
3) 4.46
4) 4.01
5) 4.47
6) 4.27
7) 3.73
8) 3.66
9) 3.58
10)None of these

Solution

Volume of 3 smaller sphere's = 3*(4/3)*Pi*r1^3
Volume of 1 Cylinder = 1*(Pi*r2^2*h1)
Volume of 2 Cones = 2*(1/3)*Pi*r3^2*h2
Volume of Larger Sphere = (4/3)*Pi*R^3

Here r1=2m, r2=3m, r3=4m, h1=4m, h2=3m, and R=?
Volume of Larger Sphere = Volume of 3 smaller sphere's + Volume of one Cylinder +Volume of 2 Cones
(4/3)*Pi*R^3 = 3*(4/3)*Pi*r1^3 + 1*P1*r2^2*h1 + 2*(1/3)*Pi*r2^2*h2

=> 4/3*R^3 = 4*8 + 36 + 32 = 100
=> R^3 = 75
R = 75^(1/3) = 4.217 =~4.22 m

Option 1)

Correct Option: 1 Best Solution (10)

05 Sep 2017 Time and Work

P can do a work in 14 days. Q can do the same work in 7 days and R can do the same in 10.5 days. Q and R start the work and leave after 3 days. P finishes the remaining work in X days. What is the value of X^2?

OPtion

1) 2.5 days
2) 1.5 days
3) 1.75 days
4) 2.0 days
5) 4.0 days
6) 4.5 days
7) 5 days
8) 5.5 days
9) 16.0 days
10) None of these

Solution

Amount of work done by Q and R in 3 days = 3*(1/7 + 2/21) = 15/21 = 5/7

Amount of work remaining after 3 days = 2/7

Amount of work done by P in 1 day = 1/14
So for 1/14 work P takes 1 day
Hence for 2/7 work P would take (1/(1/14))*2/7 = 4 days
So X=4 and X^2 =16

Correct Option: 9 Best Solution (25)

04 Sep 2017 Age

Pia's father was 28 years of age when she was born while her mother was 30 years old when her brother eleven years younger to her was born. What was the sum of ages of her parents when she was born?

OPtion

1) 57 Years
2) 58 Years
3) 47 Years
4) 48 Years
5) 49 Years
6) 56 Years
7) 46 Years
8) 45 Years
9) 46.5 Years
10)None of these

Solution

Age of Pia's father when Pia was born = 28
Age of Pia's mother when Pia was born = 30−11 =19
Required sum of ages =28+19= 47 years

Option 3)

Correct Option: 3 Best Solution (38)

01 Sep 2017 Stocks & Shares

The market value of a 14.5% stock, in which an income of Rs. 1150 is derived by investing Rs. 23000, brokerage being 3/4 %, is:

OPtion

1) 289.75
2) 289.50
3) 290.25
4) 290.75
5) 289.25
6) 290.50
7) 290.00
8) 291.25
9) 289.00
10) None of these

Solution

or an income of Rs. 1150, investment = Rs. 23000

For an income of Rs. 14.5, investment = Rs. (23000/1150) * 14.5 = 290
For a Rs. 100 stock, investment = Rs. 290

Market value of Rs. 100 stock = Rs. 290 - 0.75 = Rs. 289.25

Correct Option: 5 Best Solution (9)

31 Aug 2017 Profit and Loss

137 bananas are bought for Rs. 690 and sold at the rate of Rs. 72 per dozen. The percentage of profit or loss is:

OPtion

1) 12.8% Loss
2) 19.1% Loss
3) 19.7% Loss
4) 19.39% Loss
5) 19.5% Loss
6) 12.8% Profit
7) 19.1% Profit
8) 19.7% Profit
9) 19.39% Profit
10) None of these

Solution

Cost of 1 banana= 690/137 = 5.0364 = 5.0365
Selling price of 1 banana = 72/12 = Rs. 6

As SP > CP so its profit
So Profit % = (6 - 5.00365)*100/5.0365 = ~19.1 %
Option 7)

Correct Option: 7 Best Solution (41)