M4maths Previous Puzzles

17 Jan 2020 Speed

A boatman goes 6 km against the current of the stream in 4 hours and goes 4.5 kms along the current in 90 minutes. How long will it take to go 24 km in stationary water?

OPtion

1) 10.34 hours
2) 10.50 hours
3) 11.33 hours
4) 11.67 hours
5) 10.25 hours
6) 10 hours 20 minutes
7) 10 hours 33 minutes
8) 10 hours 66 minutes
9) 10 hours 40 minutes
10) None of these

Solution

Let the speed of boatman be x and that of current be y

Speed against current = 6/4 = x-y => x-y = 1.5
Speed with current = 4.5/1.5 = x+y=> x+y = 3

Solving we get 2x = 4.5
=> x = 2.25 and y = 0.75

Time taken in stationary water to travel 24 KMs = 24/2.25 = 10.67 = 10 hours 40 minutes

Correct Option: 9 Best Solution (3)

16 Jan 2020 Stocks

The market value of a 7.25% stock, in which an income of Rs. 1450 is derived by investing Rs. 4350, brokerage being 3/4 %, is:

OPtion

1) 21.00
2) 21.75
3) 21.75
4) 21.25
5) 20.25
6) 20.96
7) 20.75
8) 21.46
9) 21.60
10) None of these

Solution

For an income of Rs. 1450, investment = Rs. 4350

For an income of Rs. 7.25, investment = Rs. (4350/1450) * 7.25 = 21.75
For a Rs. 100 stock, investment = Rs. 21.75

Market value of Rs. 100 stock = Rs. 21.75 - 0.75 = Rs. 21


Option 1)

Correct Option: 1 Best Solution (3)

15 Jan 2020 Ratio

A 1.5 cm long grasshopper can jump 120 cm. If a 8 metre tall animal had the same height and jump
ratio, how far in centimeters could he jump

OPtion

1) 640
2) 840
3) 480
4) 720
5) 1240
6) 12800
7) 64000
8) 525
9) 880
10) None of these

Solution

8 meter = 800 cm

Jump of 8 m tall animal = (120/1.5)* 800 = 64000 cm

Correct Option: 7 Best Solution (2)

14 Jan 2020 Decode

If LOHRI = 144, PONGAL = 256 then SANKRANTI = ?

OPtion

1) 164
2) 228
3) 328
4) 264
5) 361
6) 128
7) 174
8) 184
9) 154
10) None of these

Solution

A=1, B=2, C=3....Z=26
Code = Square of first alphabets position value

For SANKRANTI = Square of position value of S = 19^2 = 361

Correct Option: 5 Best Solution (2)

13 Jan 2020 Simplify

Write (3^–8 ÷ 3^–11) ) × 3^–6 in the simplest form

OPtion

1) 3^3
2) 3^2
3) 3^4
4) 3^5
5) 3
6) 1/(3^-3)
7) 1/(3^2)
8) 1/(3^3)
9) 1/18
10) None of these

Solution

3^(–8 + 11 -6) = 3^–3
=> 1/3^3

Correct Option: 8 Best Solution (1)

10 Jan 2020 Percentage

Last year Mr. Yadav earned 212000 from the corn he grew on his farm. This year he expects a 7.5% increase in the income from corn. How much does he expect to earn from corn this year ?

OPtion

1) 221900
2) 222900
3) 217900
4) 227980
5) 221980
6) 227900
7) 223900
8) 229700
9) 227908
10) None of these

Solution

(107.5/100)*212000 = 227900

Correct Option: 6 Best Solution (8)

09 Jan 2020 Solve

Given that (3x – 8)*(3x + 2) – (4x – 11)*(2x + 1) = (x – 3)(x + 7). What is the value of 9x?

OPtion

1) 1
2) 2
3) 3
4) 6
5) 4
6) 128
7) 36
8) 8
9) 16
10) None of these

Solution

(3x - 8) (3x + 2) - (4x - 11) (2x + 1) = (x - 3) (x + 7)

⇒ (9x² + 6x - 24x - 16) - (8x² + 4x - 22x - 11) = (x² + 7x - 3x - 21)

⇒ (9x² - 18x - 16) - (8x² - 18x - 11) = x² + 4x - 21

⇒ 9x² - 18x - 16 - 8x² + 18x + 11 = x² + 4x - 21

⇒ x² - 5 = x² + 4x - 21

⇒ - 5 = 4x - 21

⇒ 4x = 21 - 5

⇒ 4x = 16

⇒ x = 16/4

⇒ x = 4

∴ the required solution be x = 4

So 9x - 4*9 = 36

Correct Option: 7 Best Solution (2)

08 Jan 2020 Solve

If x + y + z = 9 and xy + yz + zx = 20 find the value of x^3 + y^3 + z^3 - 3xyz

OPtion

1) 32
2) 49
3) 64
4) 48
5) 169
6) 181
7) 321
8) 279
9) 544
10) None of these

Solution

Given x + y + z = 9 and xy + yz + zx = 20
Consider, x + y + z = 9
Squaring on both sides, we get
(x + y + z)^2 = 9^2
x2 + y2 + z2 +2(xy + yz +zx) = 81
⇒ x2 + y2 + z2 = 81 − 2(xy + yz +zx)

=> 91 − 2(20) = 81 − 40 = 41
∴ x2 + y2 + z2 = 41
We know that x^3 + y^3 + z^3 − 3xyz = (x + y + z)( x2 + y2 + z2 − xy − yz − zx)
=> 9(41 −20) = 9(22) = 189

Correct Option: 10 Best Solution (0)

07 Jan 2020 Solve

What is the value of x^3 + y^3 + z^3 – 3xyz, when x = 2, z = –3 and y = 1 ?

OPtion

1) 1
2) 2
3) 6
4) -4
5) -6
6) 0
7) -1
8) 8
9) 4
10) None of these

Solution

x^3 + y^3 + z^3 – 3xyz = 2^3 + 1^3 + (-3)^3 - 3 *2*1*(-3)
=> 8 + 1 - 27 + 18 = 0

Correct Option: 6 Best Solution (2)

06 Jan 2020 Average

The average of Robert's marks in 6 subjects is 69.5. If his average in five subjects excluding Maths is 63.5, how many marks he obtained in Maths?

OPtion

1) 89.5
2) 90.5
3) 99.5
4) 91.5
5) 92.5
6) 93.5
7) 96.5
8) 97.5
9) 98.5
10) None of these

Solution

6*69.5 - 5*63.5 = 99.5

Correct Option: 3 Best Solution (3)