M4maths Previous Puzzles

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)

14 Jan 2022 Permutation and Combination

Find the number of ways to arrange the letters of the word 'SANKRANTI' so that all the vowels always occur together.

OPtion

1) 90720
2) 10080
3) 15120
4) 22680
5) 30240
6) 11340
7) 7560
8) 8480
9) 6420
10) None of these

Solution

In a 9 letter word SANKRANTI, there are 3 vowels i.e. two A's and one I.
Any group of letters can be arranged in n!/(P1!*P2!*..) ways, where n=Total letters and P1, P2 are number of repetitions.
We have to arrange SNKRNT (AAI) considering it a 7 letters word, where N repeats twice.
Now, these 7 letters can be arranged in 7!/2! ways with 2 repetition of N.
Vowels AAI can be arranged among themselves in 3!/2! ways with 2 repetition of A.
Hence, total number of arrangements = (7!/2!)*(3!/2!) = 7560

Correct Option: 7 Best Solution (0)

13 Jan 2022 Area & Volume

A sphere of radius 3 m is melted to form a cylinder and a cone of equal weights and heights. Find the ratio of radii of cylinder and cone.

OPtion

1) 12√3 : 1
2) √3 : 1
3) 9 : √2
4) 2 : 3
5) 1 : 3
6) 2 : √3
7) 9 : 2
8) 3 : 1
9) 1 : √3
10) None of these

Solution

Volume of Sphere = (4/3)*π*r^3 = (4/3)*π*3^3 = 36π
Given, weight and height of a cylinder & a cone is same
Hence, Volume of cylinder = Volume of cone = Volume of sphere/2 = 18π
Let radius of cylinder=r and cone=R and height=h
Volume of cylinder = π*r^2*h = 18π and
Volume of Cone = (1/3)*π*R^2*h = 18π
Comparing above volumes, we get (r/R)^2=1/3
r/R = 1/√3

Correct Option: 9 Best Solution (0)

12 Jan 2022 Mean Median Mode

Three non negative numbers A, B and C are such that the mean is X and the median is 7. If X is 12 more than the smallest number and 17 less than the biggest number, find the value of A+B+C.

OPtion

1) 42
2) 27
3) 48
4) 40
5) 29
6) 46
7) 52
8) 36
9) 30
10) None of these

Solution

Given, Median=7 of three numbers A, B and C, so middle number B=7
Mean X=(A+B+C)/3=A+12 ---(1)
Also, (A+B+C)/3=C-17 ---(2)
Now substituting value of B in above eqn. and solving (1) & (2), we get A=0, C=29
Therefore, A+B+C=0+7+29=36

Correct Option: 8 Best Solution (1)

11 Jan 2022 Number System

The sum of two numbers is 24 and the product of the two is 108. What is the square of their difference?

OPtion

1) 256
2) 100
3) 136
4) 169
5) 196
6) 225
7) 144
8) 125
9) 81
10) None of these

Solution

x+y=24 and xy=108
(x+y)^2 = x^2 + y^2 + 2xy
24^2 = x^2 + y^2 + 2*108
x^2+y^2=360
Now (x-y)^2 = x^2 + y^2 - 2xy
(x-y)^2 = 360 - 216 = 144

Correct Option: 7 Best Solution (2)

10 Jan 2022 Ratio and Proportion

For a tennis tournament, school ordered an equal number of yellow and white balls. The shop delivered 30 extra white balls, making the ratio of yellow balls to white balls 1/11 : 1/9. How many white tennis balls did the school originally order for?

OPtion

1) 165
2) 135
3) 205
4) 190
5) 270
6) 150
7) 145
8) 130
9) 155
10) None of these

Solution

Let the initial quantity of yellow and white balls each be x.
Then, x / (x+30) = (1/11) / (1/9)
Solving, we get x=135

Correct Option: 2 Best Solution (0)