M4maths Previous Puzzles

01 Jul 2022 Mensuration

Three cylinders of height of 8 cm and diameters 0.24 m, 0.28 m and 0.16 m respectively are melted to form spherical solid balls of diameter 4 cm, then number of balls thus formed is

OPtion

1) 296
2) 606
3) 315
4) 526
5) 313
6) 256
7) 303
8) 289
9) 324
10) None of these

Solution

Number of ball = Volume of three cylinders / Volume of a spherical ball
= π*8*(12² + 14² + 8²) / [(4/3) π*2³]
= 8*404 /[(4/3)*8]
= 303

Correct Option: 7 Best Solution (1)

30 Jun 2022 Time and Work

Nine men can finish a work in 20 days whereas 12 women can finish the same work in 18 days. If six men and nine women started working together. After 8 days 3 women left and 2 new men joined the work, The group continued working together till the end of the work. In how many days will they be able to do the remaining work ?

OPtion

1) 45/8
2) 72/19
3) 75/17
4) 45/11
5) 72/13
6) 84/19
7) 65/17
8) 176/13
9) 108/13
10) None of these

Solution

9 men can finish work in 20 days, so 1 man's 1 day work=1/(9x20)=1/180
12 women can finish work in 18 days, so 1 woman's 1 day work=1/(12x18)=1/216
6 men & 9 women's 8 days work=8x(6/180 + 9/216)=3/5
Remaining work=1 - 3/5=2/5
Given, after 8 days 3 women left and 2 new men joined, so in new group there are 8 men and 6 women
Now 8 men + 6 women's 1 day work=8*(1/180) + 6*(1/216) = 13/180
.'. Time required to complete remaining work = (2/5)/(13/180) = 72/13 days
Correct Option 5)

Correct Option: 5 Best Solution (2)

29 Jun 2022 Pipes & Cisterns

A pipe can fill a tank in 8 hours. After 3/5 of the tank is filled, four more pipes of half capacity are opened to fill the tank. What is the total time taken to completely fill the tank ?

OPtion

1) 5 hours 39 minutes
2) 6 hours 52 minutes
3) 5 hours 26 minutes
4) 6 hours 48 minutes
5) 6 hours 24 minutes
6) 5 hours 52 minutes
7) 5 hours 48 minutes
8) 5 hours 30 minutes
9) 6 hours 26 minutes
10) None of these

Solution

Time taken by first pipe to fill the tank = 8 hours
.'. Time taken by first pipe to fill 3/5 of the tank = (3/5)/(1/8) = 24/5 hours
Remaining part of the tank to be filled = 1 - 3/5 = 2/5
Part of the tank filled by 1 existing pipe and 4 new pipes in 1 hour = 1/8 + 4x(1/16) = 3/8
Time taken by 5 pipes to fill remaining tank = (2/5)/(3/8) = 16/15 hours
.'. Total time taken = 24/5 + 16/15 = 88/15 hours = 5 hours 52 minutes.
Correct Option 6)

Correct Option: 6 Best Solution (0)

28 Jun 2022 Algebra

If 8K⁶ + 15K³ - 2 = 0, then for positive value of K, find (K + 1/K)² = ?

OPtion

1) 4225/64
2) 65/8
3) 125/9
4) 85/4
5) 65/9
6) 45/4
7) 25/2
8) 81/16
9) 25/4
10) None of these

Solution

8K⁶ + 15K³ - 2 = 0
For simplifying & solving, let K³=x, then above equation becomes 8x² + 15x - 2 = 0
8x² + 16x -x - 2 = 0
(8x-1) (x+2) = 0
x=1/8, -2
As we require +ve value of K, so consider x=1/8
.'. K³=1/8 or K=1/2
Hence, (K + 1/K)² = (1/2 + 2)² = 1/4 + 2 + 4 = 25/4
Correct Option 9)

Correct Option: 9 Best Solution (1)

27 Jun 2022 Average

The average of some numbers is 57. If 68% of the numbers are increased by 6 and the remaining are decreased by 8, then the average so obtained will be:

OPtion

1) 58.92
2) 60.52
3) 56.26
4) 60.24
5) 58.52
6) 55.48
7) 59.52
8) 57.78
9) 57.52
10) None of these

Solution

Let there be total 'x' numbers, then new average = (57x + 0.68x*6 - 0.32x*8) / x = 58.52

Alternate Method:
Let there be 100 numbers and their average is 57, Sum=5700
For 68 numbers average=(57+6)=63, Sum=68*63=4284
For remaining 32 numbers average=(57-8)=49, Sum=32*49=1568
New average = (4284+1568)/100 = 58.52
Correct Option 5)

Correct Option: 5 Best Solution (1)

24 Jun 2022 Time Distance & Speed

A train crosses a man running in opposite direction in 21 seconds and same train crosses a 240 meters long platform in 33 seconds. If speed of man is 15 km/hr, then speed of train is

OPtion

1) 100.50 km/hr
2) 96.25 km/hr
3) 94.25 km/hr
4) 89.50 km/hr
5) 86.75 km/hr
6) 93.50 km/hr
7) 90.75 km/hr
8) 98.25 km/hr
9) 99.75 km/hr
10) None of these

Solution

Given, speed of man=15 km/hr=15*(5/18)=25/6 m/s
Let speed of train = x m/s
Relative speed of train w.r.t. man = (x + 25/6) m/s
Length of train = Time taken to cross man * Relative speed = 21*(x + 25/6)
Also, given train crosses 240 m platform in 33 sec
Length of (train+Platform) = Time taken to cross platform * Speed of train
21*(x + 25/6) + 240 = 33*x
21x + 175/2 + 240 = 33x
x = 655/24 m/s = (655/24)*(18/5) = 98.25 km/hr
Correct Option 8)

Correct Option: 8 Best Solution (0)

23 Jun 2022 Time and Work

A and B undertook a work for Rs. 11,500. When they worked together A got Rs. 2,300 less than B and A takes 7 days more than B, when they work individually. In how many days A and B working together can do the whole work ?

OPtion

1) 7⅗
2) 6⅓
3) 10½
4) 7⅘
5) 9⅔
6) 8⅖
7) 7⅓
8) 5⅓
9) 10⅖
10) None of these

Solution

Let A got Rs. x, then B Rs. (x+2300), then x + (x+2300)=11500
⇒ x=4600
Thus A got Rs. 4600 and B Rs. 6900 according to their share in work.
.'. Efficiency of A and B = 4600 : 6900 = 2 : 3
Ratio of number of days to complete the work by A and B = 1/2 : 1/3 = 3 : 2
Given, A takes 7 days more than B, so 3a - 2a=7 ⇒ a=7
Thus individually A takes 21 days and B takes 14 days
1 day's work of A and B = 1/21 + 1/14 = 5/42
Hence, A and B together can complete the work in 42/5 = 8⅖ days.

Correct Option: 6 Best Solution (1)

22 Jun 2022 Clocks and Calendars

On 22/06/2022, Mr. Samay sets the clock right at 22:06 hrs. If the clock looses 6 seconds in every 22 minutes, what will be the exact time when clock shows 22:06 hrs next day ?

OPtion

1) 21:53:26
2) 22:06:54
3) 21:56:24
4) 22:12:34
5) 22:10:58
6) 22:09:12
7) 22:18:51
8) 21:12:34
9) 22:08:34
10) None of these

Solution

Given, clock looses 6 minutes in every 22 minutes.
⇒ When actual time is 22x60 sec=1320 sec, Clock shows (22x60-6) sec =1314 sec
Time between 22:06 hrs of today and tomorrow=24 hrs=24x3600 sec
.'. When clock shows 24x3600 sec, actual time=24x3600x(1320/1314)=86794.5205 sec
Now 86794.5205 sec=24 hrs 6 min 34 sec
⇒ Actual time is 6 min 34 sec ahead of 22:06 hrs i.e 22:12:34
Correct Option 4)

Correct Option: 4 Best Solution (0)

21 Jun 2022 Arithmetic

To celebrate International Yoga day, the students of Sanskriti School gathered in a ground where they are arranged in rows to perform Yogasanas. If 2 students are extra in a row, there would be 3 row less. If 4 students are less in a row, there would be 9 rows more. Find the number of students in a school.

OPtion

1) 448
2) 532
3) 450
4) 384
5) 420
6) 468
7) 480
8) 432
9) 396
10) None of these

Solution

Let the number of rows be x and number of students in a row be y.
Total students of the school= Number of rows * Number of students in a row = xy
Case 1:
Total number of students=(x−3)(y+2)
⇒ xy=(x−3)(y+2)
2x−3y = 6 -----(i)
Case 2:
Total number of students=(x+9)(y−4)
⇒ xy=(x+9)(y-4)
-4x+9y = 36 -----(ii)
Solving equations (i) & (ii), we get, x=27, y=16
.'. Total students = xy = 27*16 = 432
Correct Option 8)

Correct Option: 8 Best Solution (2)

20 Jun 2022 Ratio & Proportion

School A has boys to girls in the ratio 5 : 6 and school B has girls to boys in the ratio 8:7. If the number of students in school A is at least twice as many as the number of students in school B, what is the minimum percentage of boys when both schools are considered together?

OPtion

1) 37.5%
2) 33.33%
3) 39.17%
4) 34.39%
5) 48.32%
6) 45.86%
7) 48.08%
8) 54.17%
9) 36.06%
10) None of these

Solution

Let school A has Boys=5x, Girls=6x and school B has Boys=7y, Girls=8y
Given, number of students in school A is at least twice as many as the number of students in school B and we have to find minimum percentage of boys out of total students.
For the minimum percentage, we need to consider the other extreme-where school A has exactly twice as many students as school B.
⇒ (5x + 6x) = 2*(7y + 8y)
y=(11/30)*x
Now total boys=5x+7y=5x+7*(11/30)*x=(227/30)*x
Total students of school A & B = 11x+15y = 11x + 15*(11/30)*x = (33/2)*x
.'. Minimum percentage of boys = [(227/30)*x / (33/2)*x]*100 = 45.86%

Correct Option: 6 Best Solution (0)