M4maths Previous Puzzles

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)

21 Jan 2022 Pipes & Cisterns

Two inlet pipes lead into a large water tank. First pipe can fill the tank in 1 hour 20 minutes; the second pipe can fill it in 50 minutes. At 10:20 am, the first pipe is opened. At what time second one should be opened so that tank gets full by 11:00 am ?

OPtion

1) 10:45
2) 10:40
3) 10:30
4) 10:50
5) 10:25
6) 10:55
7) 10:35
8) 10:42
9) 10:54
10) None of these

Solution

Starting from 10:20 am, tank is to be filled by 11:00 am i.e. in 40 min.
Filling capacity per minute of first pipe=1/80 and of second pipe=1/50
First pipe will fill for total 40 min. and second say opened after 't' min, then 40*(1/80) + (40-t)*(1/50) = 1
Solving, we get t=15
Therefore, second pipe is opened after 15 minute i.e. at 10:35 am.

Correct Option: 7 Best Solution (2)

20 Jan 2022 Average

When a boy weighing 47 kg left a group, the average weight of the remaining 49 students increased by 300g. What is the average weight of the remaining 49 boys?

OPtion

1) 60.7
2) 60.3
3) 61.7
4) 61.3
5) 60.5
6) 62
7) 60
8) 61
9) 63
10) None of these

Solution

After leaving of a boy, remaining boys are 49 i.e. There were earlier 50 boys.
Let the average of 50 boys be 'x' kg, then their total weight = 50x
Average of remaining 49 boys = (50x - 47)/49 = x+0.3
50x - 47 = 49x + 14.7
x = 61.7
Therefore, average of remaining 49 boys = 61.7 + 0.3 = 62 kg.

Correct Option: 6 Best Solution (1)

19 Jan 2022 Ratio and Proportion

Ajay, Bala and Chatur have efficiencies of work in the ratio 3 : 4 : 7. Ajay started doing a piece of work alone. After 3 days Bala joined him. After 3 more days Chatur joined them. After 6 more days work got finished. For the complete work they together received Rs. 22800. What will be the share of Chatur ?

OPtion

1) 7200
2) 9300
3) 7800
4) 8100
5) 8700
6) 7500
7) 9600
8) 8400
9) 10200
10) None of these

Solution

Given efficiencies of Ajay, Bala & Chatur in the ratio 3:4:7
Let Ajay, Bala and Chatur finish 3x, 4x and 7x work in a day respectively.
As per given information, Ajay started doing a piece of work alone, after 3 days Bala joined him, after 3 more days Chatur joined them. After 6 more days work got finished.
This means Ajay worked for 12 days, Bala for 9 days and Chatur for 6 days.
Work done by Ajay = 12*3x = 36x
Work done by Bala = 9*4x = 36x
Work done by Chatur = 6*7x = 42x
Therefore, share of Chatur = 22800*42x/(36x+36x+42x) = 8400 Rs.

Correct Option: 8 Best Solution (1)

18 Jan 2022 Sequence & Series

In the letter arrangement ABBBCCCCCDDDDDDD...... what will be letter at the place 145 ?

OPtion

1) K
2) M
3) L
4) J
5) N
6) P
7) O
8) I
9) Q
10) None of these

Solution

We can observe that, count of the letters forms the pattern like 1A, 3B, 5C, 7D, ..... which is in A.P. with difference of 2.
Now to get the 145th letter, we can find the sum of an A.P. for how many terms it gives sum=145
Sum of A.P. = (n/2)[2a + (n-1)d], where n=Number of terms, a=First term, d=Difference
145 = (n/2)[2*1 + (n-1)*2]
n^2 = 145
12 < n < 13
Thus, for 'n' we get the value more than 12 but less than 13, so 13th letter 'M' will be at 145th position in the series.

Correct Option: 2 Best Solution (3)

17 Jan 2022 Time Distance & Speed

Mohit covered a distance of 360 km between two cities, taking a total of 13 hours 30 minutes. If part of the distance was covered at 50 km per hour speed and the rest at 60 km per hour speed. How many hours did he travel at 60 km per hour?

OPtion

1) 4 hours 30 minutes
2) 3 hours 45 minutes
3) 5 hours 30 minutes
4) 4 hours 15 minutes
5) 3 hours 30 minutes
6) 5 hour 45 minutes
7) 8 hours
8) 9 hours
9) 7 hours
10) None of the above

Solution

Let Mohit travel 'x' hours at 50 km per hour.
As the total time taken to cover 720 km is 13.5 hours, he would have traveled (13.5-x) hours at 60 km per hour.
Distance covered at 50 km per hour = 50x km.
Distance covered at 60 km per hour = 60*(13.5-x) = 810 - 60x km.
Total distance covered = Distance covered at 50 km per hour + Distance covered at 60 km per hour.
720 = 50x + 810 - 60x
10x = 90
x = 9
Hence, the time for which he travel at 60 km/hr = 13.5 - 9 = 4.5 hours = 4 hours 30 minutes.

Correct Option: 1 Best Solution (1)