M4maths Previous Puzzles

28 Feb 2018 Volume

4 solid spheres of radius 1 m, 2 solid cylinders of radius 4 m, height 2 meter and 1 solid cone of radius 2 m, height 4 m are melted to form a bigger solid sphere. What is the radius of this bigger solid sphere in meters?

OPtion

1) 3.08
1) 3.22
2) 3.14
3) 3.88
4) 3.80
5) 3.87
6) 3.27
7) 3.73
8) 3.83
9) 3.58
10)None of these

Solution

Volume of 4 smaller sphere's = 4*(4/3)*Pi*r1^3
Volume of 2 Cylinders = 2*(Pi*r2^2*h1)
Volume of 1 Cone = 1*(1/3)*Pi*r3^2*h2
Volume of Larger Sphere = (4/3)*Pi*R^3

Here r1=1m, r2=4m, r3=2m, h1=2m, h2=4m, and R=?
Volume of Larger Sphere = Volume of smaller sphere's + Volume of Cylinders +Volume of Cone
(4/3)*Pi*R^3 = 4*(4/3)*Pi*r1^3 + 2*P1*r2^2*h1 + 1*(1/3)*Pi*r3^2*h2

=> 4/3*R^3 = 4*(4/3)*1 + 2*16*2 + (1/3)*4*4 = (16/3) + 192/3 + 16/3
=> R^3 = 4 + 48 + 4
=> R^3 = 56
R = 3.826 m = ~ 3.83m


Option 8)

Correct Option: 8 Best Solution (0)

27 Feb 2018 Population

The present population of a district is 325000. If it rises to 572761 during next 5 years, then find uniform rate of growth in population.

OPtion

1) 10.5
2) 11.0
3) 11.5
4) 12.33
5) 12.5
6) 12.0
7) 13.33
8) 13.0
9) 13.5
10) None of these

Solution

Population after n years = P[1+R/100]^n
=> 572761 = 325000 [1+R/100]^5
=> 1.762342 = [1+R/100]^5
=> [1+R/100] = 1.12
=> R = 12%

Correct Option: 6 Best Solution (0)

26 Feb 2018 LCM

Two numbers are in the ratio 3 : 7. If their L.C.M. is 231. What is sum of the numbers?

OPtion

1) 111
2) 105
3) 108
4) 121
5) 109
6) 120
7) 115
8) 112
9) 100
10) None of these

Solution

Let the numbers be 3x and 7x
LCM of 3x and 7x is 21x
So as per question 21x = 231
=> x= 11
3x = 3*11 = 33 and 7x = 7*11 = 77
Sum of the numbers = 33+77 = 110

Correct Option: 10 Best Solution (0)

23 Feb 2018 Ratio

Eena, Meena and Deeka start a spa with their investment ratio of 11:7:21. Eena withdraws her investment after 7 month. If profit is distributed between them yearly, then ratio of profit of Deeka and profit of Eena in the business is

OPtion

1) 66:49
2) 36:13
3) 4:1
4) 3:1
5) 66:23
6) 36:22
7) 17:6
8) 36:11
9) 66:31
10) None of these

Solution

The effective proportion of Eena= 11 * 7 (month)
the effective proportion of Meena = 7 * 12 (month)
And the effective proportion of Deeka = 21 * 12 (month)
Hence Ratio of Deeka : Eena = 21*12 : 11*7 = 36:11

Option 8)

Correct Option: 8 Best Solution (0)

22 Feb 2018 Direction Sense

Radha walks 6 km towards South. Then she turns right and walks 7 km. After this she turns to South and walks 9 km. Then she turns towards west and walks 5 km. How far is she from the starting point?

OPtion

OPTION
1) 15
2) 15.29
3) 12
4) 19.85
5) 20.12
6) 19.21
7) 20.89
8) 20.21
9) 19.59
10) None of these

Solution

As per question Radha starts from Point A and moves to Point B in south by travelling 7 KM. Then she turns right and travels 7KM to reach point C. Then she turns south and reaches point D by travelling 6 KMs. Finally turns west and travels 5 KMS to reach the final point E

Horizontal distance betwween AE = 7+5 =12
Vertical distance between AE= 9+6 = 15
We need to find distance between A and E = Sq. root (12^2 + 15^2 ) = 19.21 KMS

A
| 6
___________|
| C 7 B
9 |
______|
E 5 D

Correct Option: 6 Best Solution (0)

21 Feb 2018 Simplification

There are two buildings P and Q. If 93 persons are sent from P to Q, then the number of persons in each building is the same. If 109 persons are sent from Q to P, then the number of persons in P is double the number of persons in Q. How many persons are there in building P?

OPtion

1) 511
2) 725
3) 655
4) 699
5) 513
6) 465
7) 640
8) 675
9) 550
10) None of these

Solution

Let number of persons in building P be P and
number of persons in building Q be Q

P-93 = Q+93
=> P = Q + 186 ---- (i)

P+109= 2(Q-109)
=> P + 327 = 2Q ---- (ii)

Putting value of P from (i) in (ii)
Q + 186 + 327 = 2Q
Q = 513
P = 699

Correct Option: 4 Best Solution (0)

20 Feb 2018 Stocks

Ritika invests a part of Rs. 24,000 in 10% stock at Rs. 110 and the remainder in 15% stock at Rs. 120. If her total dividend per annum is Rs. 2700, how much does she invest in 10% stock at Rs. 110?

OPtion

1) Rs. 8000
2) Rs. 8800
3) Rs. 15000
4) Rs. 15200
5) Rs. 9000
6) Rs. 9200
7) Rs. 14000
8) Rs. 14200
9) Rs. 8600
10)Rs. None of these

Solution

Let investment in 10% stock be Rs. x.
Then, investment in 15% stock = Rs. (24000 - x).
Therefore (10/110)*x + (15/120)(24000 - x) = 2700
=> x/11 + 1/8(24000-x) = 2700
=> -3x/88 + 3000 = 2700
solving
=> x = 8800

Option 2)

Correct Option: 2 Best Solution (0)

19 Feb 2018 Divisibility

How many numbers between 1 and 100 (inclusive) are divisible by 10 or 7?

OPtion

1) 25
2) 26
3) 24
4) 22
5) 23
6) 22
7) 21
8) 27
9) 20
10) None of these

Solution

There are 10 numbers divisible by 10 between 1 and 100, and 14 numbers divisible by 7 between 1 and 100.

So there are 10 + 14 = 24, so 24 numbers divisible by one or the other, but this also includes every number which is divisible by both 7 and 10 twice.
Only one such number between 1 and 100 which is divisible both by 7 and 10 is 70

So answer is 10+14-1 = 23

Correct Option: 5 Best Solution (0)

16 Feb 2018 Simple Interest

What is the simple interest on Rs 2018 for a period of 2 years where rate of interest is 16%?

OPtion

1) 2663.76
2) 2666.76
3) 2668.76
4) 2660.76
5) 2669.76
6) 645.76
7) 647.76
8) 649.76
9) 643.76
10) None of these

Solution

SI = PRT/100 = 2018*2*16/100
= 645.76

Correct Option: 6 Best Solution (0)

15 Feb 2018 Volume

Given that length of longest diagonal of a cube is 9 cm. Find the volume of the cube?

OPtion

1) 140.40
2) 141.30
3) 140.20
4) 140.30
5) 139.30
6) 139.20
7) 142.20
8) 142.30
9) 140.50
10) None of these

Solution

Length of longest diagonal is l = a*3^1/2
volume V= a^3
Therefore, V=(l^3)/(3*3^1/2)

Given longest diagonal is:9 cm

Volume = 9^3/(3*3^1/2) = 140.30

Correct Option: 4 Best Solution (0)