M4maths Previous Puzzles

04 Feb 2022 Permutation & Combination

How many four letter words can be formed using the letters of the word 'PANTHER', if it is given that the four letter word contains alphabets T and H paired together, with T coming before H and repetition of alphabets is not allowed?

OPtion

1) 72
2) 90
3) 60
4) 75
5) 45
6) 80
7) 120
8) 150
9) 180
10) None of these

Solution

Out of the 4 letters, at two consecutive places T & H can be placed as TH _ _, _ TH _, _ _ TH, so number of ways = 3
As two letters out of 7 have been used, we have 5 letters left for the 2 left places. So, remaining two places can be arranged in 5P2 = 5 x 4 = 20 ways (without repetition)
The number of ways to make 4 letter words = 3 x 20 = 60

Correct Option: 3 Best Solution (0)

03 Feb 2022 Area and Volume

A largest square play court is prepared inside a circular ground of radius 8 m. The cost (in Rs) of making court at the rate of Rs. 120 per m² is

OPtion

1) 13560
2) 16530
3) 15630
4) 13650
5) 15660
6) 15330
7) 15360
8) 16350
9) 30720
10) None of these

Solution

The largest square has diagonal equal to diameter of a circle=2r=16 m.
Diagonal² = 2 x Side²
16² = 2 x Side²
Side² = 128 = Area of a square
.'. Required cost = 128 x 120 = 15360 Rs.

Correct Option: 7 Best Solution (1)

02 Feb 2022 Number System

If the arithmetic mean of two numbers x and y is 11 and the geometric mean of the same two number is 4√7. The numbers x= ? (Given, x > y)

OPtion

1) 16
2) 12
3) 14
4) 18
5) 11
6) 10
7) 8
8) 9
9) 7
10) None of these

Solution

Give, Arithmetic Mean=11, => (x+y)/2 = 11
x + y = 22 ---(1)
Geometric Mean=4√7, => √(xy) = 4√7
xy=112
Now, (x - y)² = (x + y)² - 4xy = 22² - 4*112 = 36
x - y = 6 ---(2)
Solving eqn. (1) & (2), we get x =14, y=8
So, the required number is 14.

Correct Option: 3 Best Solution (2)

01 Feb 2022 Time and Work

Jayesh can do some work in 8 hrs. Rajesh can do the same work in 12 hrs. Brajesh can do it in x hrs. All three starts working at 11:30 am. While Jayesh stops working at 1:30 pm and the remaining two complete the work at 4 pm. Brajesh alone can finish the same work in ___ hours.

OPtion

1) 18
2) 15
3) 24
4) 10
5) 20
6) 36
7) 12
8) 9
9) 8
10) None of these

Solution

All three works together between 11:30 am to 1:30 pm i.e. for 2 hrs and only Rajesh & Brajesh works between 1:30 pm to 4 pm i.e. for 2 hrs 30 min.
.'. 2 hrs work of (Jayesh+Rajesh+Brajesh) + 2½ hrs work of (Rajesh+Brajesh) = 1
2*( 1/8 + 1/12 + 1/x) + (5/2)*(1/12 + 1/x) = 1
Solving we get x=12
Therefore, Brajesh alone can finish the same work in 12 hrs.

Correct Option: 7 Best Solution (2)

31 Jan 2022 Time and Distance

A train leaves station A at 9:00 am for station B and travels at 80 kilometres per hour. At the same time another train leaves station B for station A and travels at 100 kilometres per hour. How far (in km) will the trains be apart 45 minutes before they meet?

OPtion

1) 135
2) 120
3) 156
3) 140
4) 100
5) 144
6) 160
7) 150
8) 136
9) 125
10) Insufficient data

Solution

Relative speed with which trains are approaching each other = 80 + 100 = 180 km/h.
So with a relative speed of 180 km/h, in 45 minutes they will travel (45/60)*180 = 135 km.
The trains will be 135 km apart 45 minutes before they meet.

Correct Option: 1 Best Solution (4)

28 Jan 2022 Number Series

Find the next number in the series 4, 6, 11, 24, 62, ...

OPtion

1) 95
2) 132
3) 194
4) 219
5) 114
6) 186
7) 118
8) 157
9) 188
10) None of these

Solution

Next term of the series is obtained as multiplication by 1, 1.5, 2, ... and adding 2.
4 x 1 + 2 = 6
6 x 1.5 + 2 = 11
11 x 2 + 2 = 24
24 x 2.5 + 2 = 62
So, next number = 62 x 3 + 2 = 188

Correct Option: 9 Best Solution (1)

27 Jan 2022 Time Distance & Speed

A train covers a certain distance at a uniform speed. If the train had been 8 kilometre per hour faster, it would have taken 3 hour less than the scheduled time and if the train was slower by 8 kilometre per hour it would have taken 5 hour more than the schedule time. Find length of the journey.

OPtion

1) 620
2) 540
3) 480
4) 650
5) 720
6) 630
7) 420
8) 384
9) 360
10) None of these

Solution

Let the speed of the train be 'x' km/h and the time taken by train to travel the given distance be 't' hours and the total distance be 'd' km. We know that, Distance=Speed*Time​
.'. d=x*t
According to 1st case: (x+8)*(t-3) = d
-3x + 8t = 24 ------(1)
Similarly, according to 2nd case: (x-8)*(t+5) = d
5x - 8t = 40 ----(2)
Solving eqn. (1) & (2), we get x=32, t=15
Hence, total length of the journey = d = x*t = 32*15 = 480 km.

Correct Option: 3 Best Solution (0)

26 Jan 2022 Coding and Decoding

In a certain language SECULAR is written as RBMVDFS, then how will REPUBLIC be written as in that language ?

OPtion

1) CJMAVOFR
2) QBKCVQFR
3) XHMCVQDW
4) OHQVCMHF
5) QBMCVQFW
6) OHKCVQFW
7) CJMCVQFR
8) PHOCVQKR
9) CJZCVQFW
10) None of these

Solution

In this coded language first and last letters have been interchanged while the remaining letters are coded by taking their immediate next letters in the reverse order.
Thus for the word REPUBLIC interchanging first and last letters we have C _ _ _ _ _ _ R
Now taking next letter of the remaining 6 letters 'EPUBLI' in reverse order, we have J M C V Q F
Therefore, correct answer is 'CJMCVQFR'

Correct Option: 7 Best Solution (0)

25 Jan 2022 Time and Work

A alone would take 4 hours more to complete a job than both A and B would together. If B worked alone, he took 9 hours more to complete it than both A and B worked together. What time (in hrs) would they take if both worked together?

OPtion

1) 12
2) 10
3) 14
4) 8
5) 9
6) 5
7) 7
8) 6
9) 7.5
10) None of these

Solution

Let time taken by A and B together be 't' hours
Thus, time taken by A = (t+4) hrs and time taken by B = (t+9) hrs
Now, equating work done by A and B in 1 hour:
1/(t+4) + 1/(t+9) = 1/t
Solving, we get, t=6 hours.

Correct Option: 8 Best Solution (1)

24 Jan 2022 Area and Volume

Water is flowing at the rate of 15 km/h through a pipe of diameter 28 cm into a rectangular tank which is 44 m long and 28 m wide. Find the time (hours) in which the level of water in the tank will rise by 50 cm.

OPtion

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

Solution

Pipe is in the form of cylinder
Rate of flow of water = 15 km/hr = 15000 m/hr
Volume of water flowing per hour = π r^2*h = (22/7)*(14/100)*(14/100)*15000 = 924 m^3
Volume of water to be filled in rectangular tank = 44*28*(50/100) m^3 = 616 m^3
So required time = 616/924 hrs = 2/3 hrs = 40 min.
Correct option 10) None of these

Correct Option: 10 Best Solution (0)