M4maths Previous Puzzles

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)

17 Jun 2022 Average

The average of 14 number is 47. The average of the last five numbers is 50 and that of first six numbers is 44. The ninth number is 3 less than the seventh number but 6 more than the eighth number. The average of eighth and ninth number is:

OPtion

1) 47.5
2) 50.5
3) 51.5
4) 48.5
5) 48
6) 51
7) 46
8) 49
9) 45
10) None of these

Solution

Total of 14 numbers = 14*47 = 658
Total of 7th, 8th, 9th number = 658 - Total of last five numbers - Total of first six numbers = 658 - 5*50 - 6*44 = 144
Let the 9th number=x, then 7th number=x+3 and 8th number=x-6
.'. Sum of 7th, 8th & 9th number = x+(x+3)+(x-6) = 144
⇒ 3x - 3=144 or x=49
Hence average of 8th & 9th number = [(x-6)+x]/2 = (43+49)/2 = 46
Correct Option 7)

Correct Option: 7 Best Solution (2)

16 Jun 2022 Algebra

If x + y = 10 and 1/x + 1/y = 12/5, then x³ + y³ = ?

OPtion

1) 587
2) 785
3) 578
4) 857
5) 685
6) 875
7) 758
8) 658
9) 865
10) None of these

Solution

Given, x+y=10
1/x + 1/y = 12/5
⇒ (x+y) / xy = 12/5
10/xy = 12/5
xy = 25/6
Now, x³ + y³ = (x + y)(x² − xy + y²)
.' (x+y)² = 10²
x² + y² + 2xy = 100
⇒ x² + y² = 100 - 2xy
.'. x³ + y³ = 10*(100 - 2xy − xy) = 10*[100 - 3*(25/6)] = 875

Correct Option: 6 Best Solution (0)

15 Jun 2022 Alligation and Mixture

In a vessel there is 170 liters of mixture of milk and water in the ratio 12:5. A certain quantity of mixture is taken out and same amount of water is added to it, then the ratio of milk and water becomes 48:37. The amount of water in final mixture (in liters) is

OPtion

1) 34
2) 50
3) 96
4) 74
5) 48
6) 72
7) 68
8) 37
9) 130
10) None of these

Solution

In initial mixture of 170 L, Quantity of milk=170*12/17=120 L and water=(170-120)=50 L
Let 'x' L of mixture is taken out and replaced by 'x' L of water
Then, new ratio of milk & water = [120 - x*(12/17)] / [50 - x*(5/17) + x] = 48/37
(170 - x) / (850 + 12x) = 4/37
6290 - 37x = 3400 + 48x
85x = 2890
x = 34
.'. Amount of water in final mixture = 50 - x*(5/17) + x = 50 - 34*(5/17) + 34 = 74 L
Correct Option 4)

Correct Option: 4 Best Solution (2)

14 Jun 2022 Percentage

To increase sales, Unique Electronics & Gadgets store offered an innovative discounts plan on marked price of an items in a month of February. The condition of discount is such that customer can avail two consecutive discounts equal to dates of booking confirmation and actual purchase. Mr. X purchased a laptop for Rs. 57,375 whose marked price is Rs. 85,000, then what are the booking confirmation and purchase dates of Mr. X, if it is known that these dates are multiple of 5 ?

OPtion

1) 5th ,15th
2) 20th, 25th
3) 15th, 25th
4) 10th,15th
5) 15th, 20th
6) 5th,10th
7) 10th, 25th
8) 10th, 20th
9) 5th, 25th
10) None of these

Solution

In the month of February dates which are multiple of 5 are 5, 10, 15, 20 and 25
So, his booking confirmation and actual purchase dates can be (5,10) (5,15) (5,20) (5,25) (10,15) (10,20) (10,25) (15,20) (15,25) (20,25)
Now check consecutive discounts of which two dates results into a purchase price of Rs. 57,375 when marked price is Rs. 85,000
For dates 5,10 : 85000x(95/100)x(90/100) = 72675
For dates 5,15 : 85000x(95/100)x(85/100) = 68637.5
For dates 5,20 : 85000x(95/100)x(80/100) = 64600
For dates 5,25 : 85000x(95/100)x(75/100) = 60562.5
For dates 10,15: 85000x(90/100)x(85/100) = 65025
For dates 10,20: 85000x(90/100)x(80/100) = 61200
For dates 10,25: 85000x(90/100)x(75/100) = 57375
For dates 15,20: 85000x(85/100)x(80/100) = 57800
For dates 15,25: 85000x(85/100)x(75/100) = 54187.5
For dates 20,25: 85000x(80/100)x(75/100) = 51000
Therefore, his booking and purchase dates are 10th and 25th respectively.
Correct Option 7)

Correct Option: 7 Best Solution (1)

13 Jun 2022 Sequence & Series

What number should replace the question mark?
167, 111, 69, 39, 19, ?

OPtion

1) 11
2) 10
3) 12
4) 9
5) 13
6) 8
7) 6
8) 5
9) 7
10) None of these

Solution

167 - (8x7) = 111
111 - (7x6) = 69
69 - (6x5) = 39
39 - (5x4) = 19
19 - (4x3) = 7

Alternate Solution:
167 111 69 39 19 7
1st Difference: 56 42 30 20 12
2nd Difference: 14 12 10 8

Correct Option: 9 Best Solution (1)