M4maths Previous Puzzles

27 May 2022 Time Distance & Speed

Train A travelling at 81 kmph overtakes another train B, 230 metre long and completely passses it in 104 seconds. If the trains had been going in opposite directions, they would have passed each other in 13 seconds. The length (in metre) of A and the speed (in Kmph) of B are respectively

OPtion

1) 210 ; 42
2) 290 ; 35
3) 320 ; 35
4) 290 ; 17.5
5) 275 ; 42
6) 320 ; 63
7) 245 ; 35
8) 290 ; 63
9) 290 ; 42
10) None of these

Solution

Speed of train A = 81 kmph = 81*5/18 = 45/2 m/s. Let the speed of train B = x m/s
Relative speed in same direction=(45/2 - x) m/s
If the length of train A be 'y' metres, then time taken to cross in same direction = (y+230)/(45/2 - x) = 104 sec.
⇒ 104x + y = 2110 ---(i)
Relative speed in opposite direction=(45/2 + x) m/s
Time taken to cross in opposite direction = (y+230)/(45/2 + x) = 13 sec.
⇒ 26x - 2y = -125 ---(i)
Solving eqn. (i) & (ii), we get x=17.5 , y=290
Speed of train B in kmph = 17.5*18/5 = 63 kmph.

Correct Option: 8 Best Solution (1)

26 May 2022 Algebra

If x + 1/x = 5/2, then possible value of x^5 + 1/x^2 is

OPtion

1) 16.03125
2) 4.0625
3) 32.125
4) 4.125
5) 32.25
6) 8.03125
7) 4.25
8) 16.125
9) 8.125
10) None of these

Solution

x + 1/x = 5/2
2x² - 5x + 2 = 0
(x-2) (2x-1) = 0
⇒ x=2 or 1/2
For x=2, x^5 + 1/x^2 = 2^5 + 1/2^2 = 32 + 0.25 = 32.25
For x=1/2, (1/2)^5 + 1/(1/2)^2 = 0.03125 + 4 = 4.03125
So, from the given options 32.25 is correct

Correct Option: 5 Best Solution (1)

25 May 2022 Time and Work

A can work 4/3 as fast as B and C together. A and B together can work 6 times as fast as C. If all three of them complete a job in 100/7 days, then how long would B alone take to complete the same work (in days)?

OPtion

1) 75
2) 60
3) 40
4) 25
5) 90
6) 80
7) 45
8) 50
9) 100
10) None of these

Solution

A, B and C together complete a job in 100/7 days
.'. 1/A + 1/B + 1/C = 7/100 ----(i)
A and B together can work 6 times as fast as C
1/A + 1/B = 6/C ----(ii)
A can work 4/3 as fast as B and C together
1/A = (4/3)*(1/B + 1/C) ⇒ 1/B + 1/C = (3/4)(1/A) ----(iii)
Substituting 1/A + 1/B = 6/C from eqn (ii) in eqn. (i), we get 6/C + 1/C = 7/100
⇒ 1/C=1/100
Substituting 1/B + 1/C = (3/4)(1/A) from eqn (iii) in eqn (i), we get 1/A + (3/4)(1/A) = 7/100
⇒ 1/A=1/25
.'. 1/25 + 1/B + 1/100 = 7/100
⇒ 1/B=1/50
Therefore, B would take 50 days to complete the work alone.

Correct Option: 8 Best Solution (0)

24 May 2022 Average

In a class there are certain number of students and their average weight is 15 kg. If 6 students with average weight of 18 kg join or 9 students with average weight of 14 kg leaves, then in both the cases average weight of students remains same. How many students are there initially in a class ?

OPtion

1) 48
2) 36
3) 42
4) 39
5) 24
6) 30
7) 33
8) 21
9) 27
10) None of these

Solution

Initially if there are 'x' students in a class, then their total weight = 15x kg.
When 6 students of average weight 18 kg joins, then average of all students = (15x + 18*6) / (x+6) Kg
When 9 students of average weight 14 kg leaves, then average of all students = (15x - 14*9) / (x-9) Kg
As both cases,the averages are same .'. (15x + 18*6) / (x+6) = (15x - 14*9) / (x-9)
(5x + 36) / (x+6) = (5x - 42) / (x-9)
5x² - 45x + 36x - 324 = 5x² - 42x + 30x - 252
3x = 72
x = 24
Hence, there are 24 students initially in a class.

Correct Option: 5 Best Solution (2)

23 May 2022 Ratio & Proportion

To celebrate party, Akshay placed an order for 9 pizzas which includes brand A and brand B pizzas. Price of brand A pizza is double that of brand B. When the order was delivered he found that the number of pizzas of the brands were interchanged and this increased the bill by 25%. The ratio of brand A and brand B pizzas in original order was

OPtion

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

Solution

Let the number of pizzas of brand B=n and brand A=(9-n)
If price of one pizza of brand B = Rs. x and brand A=2x
Then price of original order = Rs. [nx + (9-n)*2x]
Bill after interchanging the number of two brands = Rs. [n*2x + (9-n)*x]
Given, new bill is 25% more than the original
⇒ [n*2x + (9-n)*x] = (125/100)*[nx + (9-n)*2x]
n + 9 = (5/4)*(18-n)
n = 6
.'. Number of brand A=(9-n)=3 and brand B=6
Required ratio = A : B = 3:6 = 1:2
Correct Option 8)

Correct Option: 8 Best Solution (1)

20 May 2022 LCM & HCF

The ratio of sum to the LCM of two natural numbers is 12:35. If their HCF is 6, then the smaller number is

OPtion

1) 24
2) 42
3) 54
4) 30
5) 48
6) 12
7) 36
8) 18
9) 60
10) None of these

Solution

Let the numbers be 6x and 6y where x and y are prime to each other.
Then, LCM = 6xy
(6x + 6y) / 6xy = 12/35
35(x+y) = 12xy
⇒ x=5, y=7
Smallest number=6x=6*5=30
Correct Option 4)

Correct Option: 4 Best Solution (0)

19 May 2022 Time and Work

A, B and C together can complete certain work in 24 days. A and C together work twice as much as B while A and B together works four times the as much as C, then A alone can do the same work in

OPtion

1) 72 days
2) 120 days
3) 48 days
4) 30 days
5) 36 days
6) 180/7 days
7) 360/7 days
8) 90/7 days
9) 270/7 days
10) None of these

Solution

Let A, B and C can do the work in a, b and c days respectively.
Then, 1 day's work of A, B & C = 1/a + 1/b + 1/c = 1/24 ----(i)
1/a + 1/c = 2/b ----(ii)
1/a + 1/b = 4/c ----(iii)
Now subtracting (ii) from (i), we get 1/b = 1/72
Similarly subtracting (iii) from (i), we get 1/c = 1/120
Substituting values of 1/b and 1/c in (i), 1/a = 7/360
.'. A alone can do the work in 360/7 days.
Correct Option 7)

Correct Option: 7 Best Solution (1)

18 May 2022 Time Distance & Speed

A bus left point P for point Q. 70 minutes later train left P for Q and arrived at Q at the same time as the bus. If the bus and the train left simultaneously from the opposite ends P and Q towards each other, they would have met in 84 minutes after the start. How much time did it take the bus to travel from P to Q?

OPtion

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

Solution

Let distance from P and Q = d ; Speed of Bus = x ; Speed of Train = y
Let, time taken by bus to travel distance d = t min. and by train = (t-70) min.
Speed = Distance/Time
x = d/t
y = d/(t-70)
When travelling towards each other time taken=84 min.
⇒ Distance covered by bus in 84 min + Distance covered by train in 84 min = Total distance
(d/t)*84 + [d/(t-70)]*84 = d
84/t + 84/(t-70) = 1
t² - 238t + 5880 = 0
(t-28) (t-210) = 0
t=28, 210
The time 't' can not be less than 70 min as train starts 70 minutes after the bus starts and they meet after some time, .'. t = 210 min = 3 hrs 30 min.
Correct Option 7)

Correct Option: 7 Best Solution (1)

17 May 2022 Algebra

If 1/x - 1/y = -29 and the value of (x + 12xy - y) / (x - 6xy - y) can be expressed as m/n, where m and n are co prime positive integers. The value of m+n=?

OPtion

1) 52
2) 40
3) 78
4) 55
5) 68
6) 46
7) 76
8) 64
9) 56
10) None of these

Solution

1/x - 1/y = -29
(y - x)/xy = -29
y - x = -29xy or x - y = 29xy
So, (x + 12xy - y) / (x - 6xy - y) = (29xy + 12xy) / (29xy - 6xy) = 41xy/23xy = 41/23
.'. m/n = 41/23
⇒ m=41, n=23 and m+n = 41+23 = 64
Correct Option 8)

Correct Option: 8 Best Solution (0)

16 May 2022 Number Series

Find next number in the series 7, 19, 53, 151, 437, ?

OPtion

1) 1297
2) 1295
3) 1259
4) 1279
5) 1305
6) 1287
7) 1311
8) 1278
9) 1317
10) None of these

Solution

Series is formed by multiplication by 3 and subtraction of 2, 4, 8, ....
7 x 3 - 2 = 19
19 x 3 - 4 = 53
53 x 3 - 8 = 151
151 x 3 - 16 = 437
437 x 3 - 32 = 1279

Correct Option: 4 Best Solution (2)