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M4maths Previous Puzzles

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)
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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)
G.S.Kantharao   1 Month AGO
A+C=2B
A+B=4C
A+B+C=1/24
3B=1/24
B=1/72
Now 4C+C=1/24
C=1/120
A=1/24 -1/72 -1/120=7/360
So A can do in 360/7d
My option is 7👈
Like? Yes (5) | No   

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)
Pargat Pal Singh   1 Month AGO
If distance is d and time taken (in minutes) by bus to cover distance d is x, then
Speed of bus= d/x
Speed of train = d/(x-70)
When trainscstart from opposite sides simultaneously..
84*(d/x + d/(x-70)) =d
Solving it, we get,
x=210 minutes or 3 hour 30 minutes
Like? Yes (2) | No   

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)
G.S.Kantharao   1 Month AGO
Series is 7,19,53,151,437...
=7,(7*3-2),(19*3-4),(53*3-8),(151*3-16)
Si the next term is =(437*3-32)=1279
So my option is 4👈
Like? Yes (5) | No   
Dr.Dipin Singh   1 Month AGO
7x2+5=19
19x2+(5x3) = 53
53x2+(5x3x3) = 151
151x2+(45x3) = 437
437x2+(135x3) = 1279
Like? Yes (2) | No   

13 May 2022 Profit & Loss

In a End of Season Sale, to clear stock a shopkeeper offers 50 items in price of 20 items but still there is no loss or gain in this transaction. What is his usual gain percentage when there is no sale ?

OPtion

1) 50
2) 66.66
3) 133.33
4) 150
5) 250
6) 100
7) 400
8) 300
9) 200
10) None of these
Solution
Given, shopkeeper sells 50 items in price of 20 items but there is no loss or gain.
⇒ CP of 50 items = SP of 20 items
Let CP of 1 item=1, so CP of 50 items=50=SP of 20 items
.'. SP of 1 item=50/20=2.5
% profit = [(2.5-1)/1]*100 = 150%
Correct Option 4)
Correct Option: 4 Best Solution (0)

12 May 2022 LCM & HCF

LCM of two numbers is 60 times their HCF. If sum of LCM and HCF is 549. If one number is 45, then other number is

OPtion

1) 96
2) 132
3) 181
4) 162
5) 180
6) 126
7) 108
8) 216
9) 144
10) None of these
Solution
Given, one number=45 and LCM=60HCF. Let other number=x
We know, product of LCM & HCF = Product of two numbers
LCM*HCF = 45x
60HCF*HCF = 56x ----(i)
Also, LCM + HCF = 549
60HCF + HCF = 549
61HCF = 549
⇒ HCF=9
Now substituting HCF=9 in Eqn (i), we get 60*9*9 = 45x
⇒ x=108
Correct Option: 7 Best Solution (3)
G.S.Kantharao   1 Month AGO
Let H.C.F =H
L.C.M =60H
L.C.M+H.C.F=60H+H=549
H=549/61=9
L.C.M=60*9=540
Other Number=540*9/45=108
My option is 7👈
Like? Yes (4) | No   
Dr.Dipin Singh   1 Month AGO
If hcf is x, then
x+60x=549
x=9=hcf
Lcm=60x=540
One number is given as 45,
Hence other number =9*540/45= 108
Like? Yes (1) | No   
RAMADURAI NATESAN   1 Month AGO
Let Nos. be M and N. M = 45.
L = 60H. L + H = 549 = 61 H. H = 9.L = 540.
M*N = L*H =4860. N = 4860/45 =108
Like? Yes (1) | No   

11 May 2022 Number System

If P is a three digit number where first digit is three times the last digit and no digit is repeated. How many P are possible which are divisible by 6 ?

OPtion

1) 8
2) 3
3) 5
4) 2
5) 6
6) 1
7) 4
8) 9
9) 7
10) None of these
Solution
Given, 1st digit is 3 times the 3rd digit. .'. The 3-digit number can be of the form 3 _ 1 ; 6 _ 2 ; 9 _ 3
Now, for a number to be divisible by 6, it should be an even number divisible by 2 and 3 both.
.'. Only possible numbers will be even numbers of the form 6 _ 2
So, the numbers are 612, 642, 672, Total 3
Correct Option 2)
Correct Option: 2 Best Solution (1)
Akshitha priya   1 Month AGO
given the conditions only possible cases are....1) 3_1
2) 6_2
3) 9_3
no divisible by 6 should be even and the sum should be divisible by 3 .......hence option 1 and 2 rules out as it is odd only possible is 2nd and here also as the sum is already 8 now any number added sum must be divisible by 3 so...only options are...612,642,672,
Like? Yes (1) | No   

10 May 2022 Ratio & Proportion

An alloy contains magnesium, copper and zinc in the ratio 3 : 4 : 2 and another alloy contains copper, zinc and nickel in the ratio 4 : 5 : 3. If equal weights of both alloys are melted together to form a third alloy, then the weight of copper per kg in new alloy will be:

OPtion

1) 175 gm
2) 225 gm
3) 125 gm
4) 319.44 gm
5) 388.88 gm
6) 416.66 gm
7) 166.66 gm
8) 305.55 gm
9) 527.77 gm
10) None of these
Solution
In 1st alloy: Ratio of magnesium, copper, Zinc = 3 : 4 : 2
In 2nd alloy: Ratio of copper, zinc, nickel = 4 : 5 : 3
Now, let the weight of first alloy be 36 kg (taken as Magnesium=12 kg, Copper=16 kg, Zinc=8 kg) and
Weight of second alloy = 36 kg (taken as Copper=12 kg, Zinc=15 kg, Nickel=9 kg)
When two alloys are mixed in equal weights, total weight of third alloy=36+36=72 kg
Weights in 3rd alloy: Magnesium=12 kg, Copper=(16+12) kg, Zinc=(8+15) kg, Nickel=9 kg.
Weight of Copper in 3rd alloy = 28 kg per 72 kg
.'. Weight per kg = 28/72 kg = 388.88 gm..
Correct Option: 5 Best Solution (2)
G.S.Kantharao   1 Month AGO
Magnesium:copper:zinc=3:4:2
Copper:zinc:nickel=4:5:3

Now, let the first alloy be 36kg =3:4:2=(3+4+2)=9×4=12:16:8=36kg

Now second alloy be 36kg= 4:5:3=(4+5+3)=12×3=12:15:9=36kg
Now Alloys are mixed together to form third alloy. Then the ratio of content in it,
Magnesium:copper:zinc:nickel =12:28:23:9
Now third alloy weight is 36+36=72kg
Now copper weight=28/72=388.88gms
So my option is 5
Like? Yes (3) | No   
Pargat Pal Singh   1 Month AGO
If 36 kg of each alloy are mixed, then quantity of copper in final 72 kg product = 16+12=28 kg
Qnty of copper in 1 kg=28/72=0.388888 kg means 388.88 gms
Like? Yes | No   

09 May 2022 Pipes & Cisterns

A leak in the bottom of a tank can empty it in 8 hours. An inlet pipe fills the tank at the rate of 6 liters per minute. When the tank is full, the inlet is opened but leak emptied the tank in 9 hours. The capacity of the tank (in liters) is

OPtion

1) 25290
2) 24920
3) 29160
4) 24290
5) 25920
6) 29610
7) 29160
8) 21600
9) 24300
10) None of these
Solution
Let the capacity of tank = x liters
Tank emptied per hour by leakage = x/8
Tank filled per hour by inlet pipe = 6*60 = 360 litres
Effective filling per hour with inlet pipe & leakage = 360 - x/8
From the given data, in 9 hrs, full tank get emptied with inlet and leakage
.'. x + 9*(360 - x/8) = 0
(9/8)*x - x = 3240
x = 25920
Correct Option 5)
Correct Option: 5 Best Solution (1)
Varun   1 Month AGO
Inlet fills tank at 6L per minute
It was filling it for 9 hours = 9hours*60minutes*6liter = 3240
Leak empties it in 8 hours
So capacity = 3240*8 = 25920 = Option (5)
Like? Yes (1) | No   
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Challenger of the Day

G.S.Kantharao
G.S.Kantharao
India
Andhra Pradesh
Time: 00:03:33
Points
17

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