M4maths Previous Puzzles

08 Nov 2017 Profit and Loss

408 bananas are bought for Rs. 1200 and sold at the rate of Rs. 54 per dozen. The percentage of profit or loss is:

OPtion

1) 53 % Profit
2) 54 % Profit
3) 55 % Profit
4) 46 % Profit
5) 47 % Profit
6) 48 % Profit
7) 49 % Profit
8) 56 % Profit
9) 57 % Profit
10) None of these

Solution

Cost of 1 banana= 1200/408 = 2.941176

Selling price of 1 banana = 54/12 = Rs. 4.5

As SP > CP so its profit
So Profit % = (4.5 - 2.941176 )*100/2.941176 = 53 %
Option 1)

Correct Option: 1 Best Solution (0)

07 Nov 2017 Time and Work

P can do a work in 22 days. Q can do the same work in 16.5 days and R can do the same in 27.5 days. Q and R start the work and leave after 7.5 days. P finishes the remaining work in X days. What is the value of X?

OPtion

1) 5 days
2) 5.5 days
3) 7 days
4) 6.0 days
5) 6.5 days
6) 8 days
7) 4 days
8) 4.5 days
9) 7.5 days
10) None of these

Solution

Amount of work done by Q and R in 7.5 days = 7.5*(1/16.5 + 1/27.5) = 7.5*((10+6)/165) = 120/165 = 8/11
Amount of work remaining after 7.5 days = 3/11

Amount of work done by P in 1 day = 1/22
So for 1/22 work P takes 1 day
Hence for 3/11 work P would take (1/(1/22))*3/11 = 6 days

Option 4)

Correct Option: 4 Best Solution (2)

06 Nov 2017 Age

Mayanti's father was 22.5 years of age when she was born while her mother was 27.5 years old when her brother six and half years younger to her was born. What is the difference between the ages of her parents?

OPtion

1) 1 Year
2) 1.5 Years
3) 2 Years
4) 2.5 Years
5) 3 Years
6) 3.5 Years
7) 4.5 Years
8) 5 Years
9) 6 Years
10)None of these

Solution

Age of Mayanti's father when Mayanti was born = 22.5
Age of Mayanti's mother when Mayanti was born = 27.5−6.5 =21
Required difference of age =22.5−21= 1.5 Years

Option 2)

Correct Option: 2 Best Solution (1)

03 Nov 2017 Mixture

A merchant has 310 kg of sugar, part of which he sells at 2% loss and the rest at 8% profit. He gains 5% on the whole. What is the difference between the quantities of sugar sold at 8% profit and that sold at 2% loss?

OPtion

1) 93 kg
2) 186 kg
3) 100 kg
4) 72 kg
5) 62 kg
6) 124 kg
7) 90 kg
8) 88 kg
9) 217 kg
10)None of these

Solution

(Quantity of Cheaper)/(Quantity of Dearer) = (Price of Dearer - Mean Price)/(Mean Price - Price of Cheaper)

(Quantity of Cheaper)/(Quantity of Dearer) = (108 - 105)/(105-98) = 3/7

Total Quantity = 310 KG

The quantity sold at 2% loss is = (3/10) * 310 = 93 Kgs
The quantity sold at 8% loss is = (7/10) * 310 = 217 Kgs
Difference between Quantity = 217-93 = 124 Kgs


Option 6)

Correct Option: 6 Best Solution (0)

02 Nov 2017 Probability

With Dhoni and Bhuvi at the crease Cricket Team of India needs to score 7 runs in last 2 balls to win the match. What is the probability that the match would be a tie? 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) 1/9
2) 1/6
3) 11/36
4) 10/35
5) 1/3
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
It would be a tie match if India manages to score exactly 6 runs in these 2 balls.

So possible pair of runs in 2 balls which will result in a tie :
(6,0), (4,2), (2,4), (3,3), (0,6) => count of pairs = 5

Probability that it would be a tie = 5/36

Correct Option: 7 Best Solution (3)

01 Nov 2017 Bells Tolling Together

Six bells commence tolling together and toll at intervals of 2 4 6 9 10 and 12 seconds. In first 30 minutes how many times do they toll together?

OPtion

1) 16
2) 15
3) 26
4) 11
5) 10
6) 25
7) 20
8) 21
9) 24
10) None of these

Solution

Answer: 26

LCM of 2 4 6 9 10 and 12 = 180
This means that every 180 seconds the bells will toll together
So in 30 minute or 1800 seconds number of times they will toll together = 1800/180 = 10

As its mentioned that Six bells commence tolling together, so in the beginning i.e. at 0 the bells have tolled together so Answer is 10+1 = 11

Option 4)

Correct Option: 4 Best Solution (5)

31 Oct 2017 Root and Power

Find value of:
(2)^1.56 * (3)^1.78 * (7)^0.78 * (84)^0.22 = ?

OPtion

1) 226.00
2) 232.00
3) 239.33
4) 243.08
5) 248.25
6) 254.88
7) 250.00
8) 249.33
9) 2520.0
10) None of these

Solution

(2)^1.56 * (3)^1.78 * (7)^0.78 * (84)^0.22
= (2)^1.56 * (3)^1.78 * (7)^0.78 * (4*3*7)^0.22
= [(2)^1.56 * 4^0.22] * [(3)^1.78 * (3)^0.22] * [(7)^0.78 * (7)^0.22)]
= [(2)^1.56 * 2^0.22 * 2^0.22] * [(3)^1.78 * (3)^0.22] * [(7)^0.78 * (7)^0.22)]
= [2^(1.56+0.22+0.22)] * [3^(1.78+0.22)] * [7^(0.78+0.22)]
= [2^2] * [3^2] *[7^1]
= 4*9*7
= 252

Correct Option: 10 Best Solution (0)

30 Oct 2017 Profit and Loss

A vendor bought 370 chocolates for 5550 rupees. How many chocolates in 5550 rupees must he sell to gain 25%?

OPtion

1) 256
2) 296
3) 275
4) 260
5) 236
6) 300
7) 306
8) 290
9) 285
10)None of these

Solution

CP of 1 Chocolate = 5550/370 = Rs. 15
SP of 1 Chocolate for 25% profit = 15*1.25 = Rs. 18.75
So in 5550 Rupess how many chocolates should be sold = 5550/18.75 = 296

Option 2)

Correct Option: 2 Best Solution (8)

27 Oct 2017 Trains

Two trains each 365 meter long, are running in opposite directions on parallel tracks. If their speeds are 44 km/hr and 64 km/hr respectively, the square of time taken by the faster train to pass the driver of the slower one is?

OPtion

1) 12.55 seconds
2) 12.31 seconds
3) 12.93 seconds
4) 12.00 seconds
5) 12.16 seconds
6) 142.50 seconds
7) 144.26 seconds
8) 148.03 seconds
9) 149.01 seconds
10) None of these

Solution

Relative speed= 64+44 = 108 km/hr = 108 * 5/18 = 30 m/sec

We are calculating the time taken by the faster train to pass the driver of the slower one.
Hence, distance = length of the faster train = 365 metre

Time = 365/30 = 12.16 seconds
Square of time taken = (365/30) ^2 = 148.03

Option 8)

Correct Option: 8 Best Solution (5)

26 Oct 2017 Factors

How many factors of 82044596000 are odd number?

OPtion

1) 12
2) 8
3) 16
4) 18
5) 25
6) 15
7) 30
8) 40
9) 24
10) None of these

Solution

82044596000 = 2^5 * 5^3 * 29^5

Any factor of this number should be of the form 2^a * 5^b * 129^c.

For the factor to be a odd number a should be 0

b can take values 0, 1, 2, 3
and c can take values 0, 1, 2, 3, 4, 5

Total number of odd factor = 4 * 6 = 24

Correct Option: 9 Best Solution (0)