M4maths Previous Puzzles

08 Jul 2022 Average

A, B, C and D are four positive numbers such that A is 2/3 times of B, B is 5/6 times of C and C is 3/5 times of D. If the average of 3 times of A and 4 times of D is 900, then the average of all four numbers A, B, C and D is:

OPtion

1) 241.5
2) 246.5
3) 215
4) 244
5) 224
6) 208
7) 204
8) 219
9) 236
10) None of these

Solution

A=(2/3)*(5/6)*(3/5)*D
D=3A
Also, average of 3 times A and 4 times D = 900
⇒ 3A + 4D = 1800
Now substituting D=3A in above equation, we get, D + 4D = 1800
D=360
.'. A=360/3=120
B=(3/2)*A=(3/2)*120=180
C=(3/5)*D=(3/5)*360=216
Hence, average of A, B, C & D = (120+180+216+360)/4 = 876/4 = 219
Correct Option 8)

Correct Option: 8 Best Solution (1)

07 Jul 2022 Profit & Loss

A dishonest shopkeeper professes to sell at a discount of 15% to his cost price but uses 400 gm instead of 500 gm. The actual gain or loss percentage is

OPtion

1) 5.33% Loss
2) 6.75% Gain
3) 6.66% Gain
4) 6.25% Gain
5) 7.66% Loss
6) 7.33% Gain
7) 4.84% Gain
8) 3.33% loss
9) 4.25% Gain
10) None of these

Solution

For shopkeeper, let CP of 1 kg or 1000 gm = 100
As he is using 400 gm instead of 500 gm .'. For 1 kg price, he actually sells 800 gm
CP of 800 gm = 80
With 15% discount, SP of 800 gm = (100-15) = 85
.'. % Gain = [(85-80)/80]*100 = 25/4 or 6.25%
Correct Option 4)

Correct Option: 4 Best Solution (1)

06 Jul 2022 Ratio & Proportion

If A, B, and C are positive integers and 7A=4B=8C, then the least possible value of A+B+C=?

OPtion

1) 58
2) 19
3) 38
4) 56
5) 28
6) 57
7) 29
8) 87
9) 17
10) None of these

Solution

Let 7A=4B=8C=k then A=k/7, B=k/4, C=k/8.
A : B : C = k/7 : k/4 : k/8
Multiply the ratio by 56 (LCM of 7,4,8)
A : B : C = 8k : 14k : 7k
The minimum possible values of A, B & C are for k=1
.'. A=8, B=14, C=7 and minimum sum=8+14+7=29

Correct Option: 7 Best Solution (1)

05 Jul 2022 Coding & Decoding

In a certain pattern ‘FORGIVE’ is coded as ‘IMUELTH’ and 'PURPOSE' as 'SSUNRQH'. Select the right option for ‘MUNDANE’ coded in the same form?

OPtion

1) SSQBDLH
2) PSQBDHL
3) KXLGXQB
4) PPQBDLH
5) PSBQDLH
6) SSBQDHL
7) PSQBDLH
8) SPQBDHL
9) KXLGXBQ
10) None of these

Solution

When letters from A to Z are numbered from 1 to 26 respectively, the coding of letters is 3 letters forward and 2 letters backward positions alternatively.
F O R G I V E = (F+3), (O-2), (R+3), (G-2), (I+3), (V-2), (E+3) = I M U E L T H
P U R P O S E = (P+3), (U-2), (R+3), (P-2), (O+3), (S-2), (E+3) = S S U N R Q H
M U N D A N E = (M+3), (U-2), (N+3), (D-2), (A+3), (N-2), (E+3) = P S Q B D L H
Correct Option 7)

Correct Option: 7 Best Solution (1)

04 Jul 2022 Algebra

For the equation 10x² + kx + 6 = 0, if roots are in the ratio 3:4, then find positive value of k.

OPtion

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

Solution

Given equation: 10x² + kx + 6 = 0
The roots are in the ratio 3:4. Let roots of the equation are 3ɑ and 4ɑ.
Applying condition for sum and product of the roots,
Sum of roots = 3ɑ + 4ɑ = -k/10 ---(i) and
Product of roots = 3ɑ*4ɑ = 6/10 = 3/5
12ɑ² = 3/5
ɑ = ±1/(2√5)
From (i), k = -70ɑ
.'. k = -70*(-1/(2√5)) = 7√5

Correct Option: 4 Best Solution (0)

01 Jul 2022 Mensuration

Three cylinders of height of 8 cm and diameters 0.24 m, 0.28 m and 0.16 m respectively are melted to form spherical solid balls of diameter 4 cm, then number of balls thus formed is

OPtion

1) 296
2) 606
3) 315
4) 526
5) 313
6) 256
7) 303
8) 289
9) 324
10) None of these

Solution

Number of ball = Volume of three cylinders / Volume of a spherical ball
= π*8*(12² + 14² + 8²) / [(4/3) π*2³]
= 8*404 /[(4/3)*8]
= 303

Correct Option: 7 Best Solution (1)

30 Jun 2022 Time and Work

Nine men can finish a work in 20 days whereas 12 women can finish the same work in 18 days. If six men and nine women started working together. After 8 days 3 women left and 2 new men joined the work, The group continued working together till the end of the work. In how many days will they be able to do the remaining work ?

OPtion

1) 45/8
2) 72/19
3) 75/17
4) 45/11
5) 72/13
6) 84/19
7) 65/17
8) 176/13
9) 108/13
10) None of these

Solution

9 men can finish work in 20 days, so 1 man's 1 day work=1/(9x20)=1/180
12 women can finish work in 18 days, so 1 woman's 1 day work=1/(12x18)=1/216
6 men & 9 women's 8 days work=8x(6/180 + 9/216)=3/5
Remaining work=1 - 3/5=2/5
Given, after 8 days 3 women left and 2 new men joined, so in new group there are 8 men and 6 women
Now 8 men + 6 women's 1 day work=8*(1/180) + 6*(1/216) = 13/180
.'. Time required to complete remaining work = (2/5)/(13/180) = 72/13 days
Correct Option 5)

Correct Option: 5 Best Solution (2)

29 Jun 2022 Pipes & Cisterns

A pipe can fill a tank in 8 hours. After 3/5 of the tank is filled, four more pipes of half capacity are opened to fill the tank. What is the total time taken to completely fill the tank ?

OPtion

1) 5 hours 39 minutes
2) 6 hours 52 minutes
3) 5 hours 26 minutes
4) 6 hours 48 minutes
5) 6 hours 24 minutes
6) 5 hours 52 minutes
7) 5 hours 48 minutes
8) 5 hours 30 minutes
9) 6 hours 26 minutes
10) None of these

Solution

Time taken by first pipe to fill the tank = 8 hours
.'. Time taken by first pipe to fill 3/5 of the tank = (3/5)/(1/8) = 24/5 hours
Remaining part of the tank to be filled = 1 - 3/5 = 2/5
Part of the tank filled by 1 existing pipe and 4 new pipes in 1 hour = 1/8 + 4x(1/16) = 3/8
Time taken by 5 pipes to fill remaining tank = (2/5)/(3/8) = 16/15 hours
.'. Total time taken = 24/5 + 16/15 = 88/15 hours = 5 hours 52 minutes.
Correct Option 6)

Correct Option: 6 Best Solution (0)

28 Jun 2022 Algebra

If 8K⁶ + 15K³ - 2 = 0, then for positive value of K, find (K + 1/K)² = ?

OPtion

1) 4225/64
2) 65/8
3) 125/9
4) 85/4
5) 65/9
6) 45/4
7) 25/2
8) 81/16
9) 25/4
10) None of these

Solution

8K⁶ + 15K³ - 2 = 0
For simplifying & solving, let K³=x, then above equation becomes 8x² + 15x - 2 = 0
8x² + 16x -x - 2 = 0
(8x-1) (x+2) = 0
x=1/8, -2
As we require +ve value of K, so consider x=1/8
.'. K³=1/8 or K=1/2
Hence, (K + 1/K)² = (1/2 + 2)² = 1/4 + 2 + 4 = 25/4
Correct Option 9)

Correct Option: 9 Best Solution (1)

27 Jun 2022 Average

The average of some numbers is 57. If 68% of the numbers are increased by 6 and the remaining are decreased by 8, then the average so obtained will be:

OPtion

1) 58.92
2) 60.52
3) 56.26
4) 60.24
5) 58.52
6) 55.48
7) 59.52
8) 57.78
9) 57.52
10) None of these

Solution

Let there be total 'x' numbers, then new average = (57x + 0.68x*6 - 0.32x*8) / x = 58.52

Alternate Method:
Let there be 100 numbers and their average is 57, Sum=5700
For 68 numbers average=(57+6)=63, Sum=68*63=4284
For remaining 32 numbers average=(57-8)=49, Sum=32*49=1568
New average = (4284+1568)/100 = 58.52
Correct Option 5)

Correct Option: 5 Best Solution (1)