M4maths Previous Puzzles

31 Dec 2021 discount

A book seller allowed 18% discount on printed price. He gets 24% commission from publisher. His profit in per cent will be

OPtion

1. 7.8%
2. 6.2%
3. 5.8%
4. 9.3%
5. 9.6%
6. 7.2%
7. 6.8%
8. 8.8%
9. 8.6%
10. None of the above

Solution

Let the selling price = 100
Purchase price after discount = 24% = 100 – 24 = 76
After discount of 10% actual selling price = 100 – 18 = 82
Actual profit = 82 – 76 = 6
Percentage of profit = 6 x 100 /76
= 7.8%

Correct Option: 1 Best Solution (0)

30 Dec 2021 Ticket

Vijay could get equal number of ₹75, ₹95 and ₹100 tickets for a movie. He spent 6210 for all the tickets. How many of each did he buy?

OPtion

1. 12
2. 23
3. 20
4. 18
5. 17
6. 27
7. 31
8. 21
9. 25
10. None of these

Solution

Let, total tickets = t
Then, 75t + 95t+ 100t = 6210
⇒ 270t = 6210
⇒ t = 6210 /270
⇒ t = 23

Correct Option: 2 Best Solution (2)

29 Dec 2021 circular ground

A circular ground of radius 16 m has a path of width 2.8 m around it on its outside. Find the area of the path.

OPtion

1. 304.6
2. 298.8
3. 299.6
4. 300.5
5. 304.25
6. 306.2
7. 310.2
8. 315.5
9. 320.8
10. None of the above

Solution

The area of the circular path = π w(2r + w)
= 22 /7 × 2.8 × (2 × 16 + 2.8)
= 8.8 × (32 + 2.8) = 306.2 m^2

Correct Option: 6 Best Solution (0)

28 Dec 2021 Circle

Find the area of largest circle inscribed in a square of side 112 cm.

OPtion

1. 9866
2. 9842
3. 9870
4. 9888
5. 9856
6. 9850
7. 9840
8. 9360
9. 9690
10. None of the above

Solution

The area of the largest circle
= πa^2 /4
= (22 x112x x112)/ 7 x 4
= 9856 cm^2 .

Correct Option: 5 Best Solution (4)

27 Dec 2021 Cone

Two right circular cones of equal heights have their radii in the ratio of 1:3. Find out the ratio of their volumes

OPtion

1. 1:6
2. 1:44
3. 1:9
4. 2:9
5. 2:6
6. 2:3
7. 1:3
8. 3:9
9. 3:6
10. None of the above

Solution

Ratio of volumes = (Ratio of radii)^2 = (1:3)^2 = 1:9.

Correct Option: 3 Best Solution (1)

24 Dec 2021 Tiles

A hall of length 24 cm and breadth 20 m is to be paved with equal square tiles. What will be the size of the largest tile so that the tiles exactly fi t and also find the number of tiles required.

OPtion

1. 115
2. 116
3. 128
4. 134
5. 130
6. 120
7. 126
8. 110
9. 105
10. None of the above

Solution

Size of the largest possible square tile
= H.C.F. (l, b)
= H.C.F. (24, 20) = 4 m
Number of tiles required
= l x b / H.C.F. (24, 20)
= 24 x 20 / 4 = 120 tiles.

Correct Option: 6 Best Solution (1)

23 Dec 2021 Bamboo

Find out the length of the longest bamboo that can be placed in a room which is 12 m long, 12 m broad and 6 m high.

OPtion

1. 18
2. 17
3. 21
4. 23
5. 26
6. 27
7. 20
8. 15
9. 13
10. None of the above

Solution

Length of the bamboo
= length of the diagonal of the room
= √(12^2 + 12^2 + 6^2)
= √324 = 18 m.

Correct Option: 1 Best Solution (3)

22 Dec 2021 Work & Time

Ahmed is thrice as good a workman as Balkar and takes 22 days less to complete a piece of work than Balkar takes. Find out time in which Balkar alone can complete the work.

OPtion

1. 15
2. 23
3. 26
4. 22
5. 20
6. 33
7. 31
8. 29
9. 38
10. None of the above

Solution

Here, k = 3 and l = 22.
∴ Time taken by Balkar, working alone, to complete the work
= kl / (k – 1) days
= 3 x 22 / (3- 1)days,
i.e., 33 days.

Correct Option: 6 Best Solution (0)

21 Dec 2021 Permutation

In how many different ways can the letters of the word ‘NANAKMATTA’ be permuted?

OPtion

1. 37600
2. 35650
3. 37800
4. 35800
5. 34600
6. 30000
7. 29800
8. 38600
9. 36600
10. None of these

Solution

The word NANAKMATTA has 10 letters in all. The letter ‘A’ occurs 4 times, the letter ‘N’ occurs 2, letter ‘T’ occurs 2 times and the remaining two letters K & M each occur once.
∴ The require number of permutations
= 10! /4!2!2!1!1!
= 10! /4!2!2!
= (10*9*8*7*6*5*4!)/4!2*2
= (10*9*4*7*3*5)
= 37800

Correct Option: 3 Best Solution (3)

20 Dec 2021 Distance

What will be the distance between the pair of points A(2, 5) and B(–3, 7)?

OPtion

1. √29
2. √31
3. √37
4. √27
5. 5
6. √21
7. √30
8. 6
9. 7
10. None of the above

Solution

AB = √(-3-2)^2 + (7-5)^2
= √(25+4)
=√29

Correct Option: 1 Best Solution (4)