M4maths Previous Puzzles

10 Jun 2022 Number System

A number is divided into two parts such that 60% of the first part is 3 more than the 80% of second part. Also 40% of the first part is 5 less than the 65% of the second part.The number is

OPtion

1) 155
2) 140
3) 120
4) 150
5) 125
6) 145
7) 165
8) 160
9) 135
10) None of these

Solution

Let the first and second part of a number is 'a' and 'b' respectively.
According to given condition:
Case I: (60/100)*a - (80/100)*b = 3 ⇒ 3a - 4b = 15 ---(i)
Case II: (65/100)*b - (40/100)*a = 5 ⇒ 13b - 8a = 100 ---(ii)
From Eqn. (i) & (ii), a=85, b=60
Hence required number = (a + b) = 85+60 = 145

Correct Option: 6 Best Solution (1)

09 Jun 2022 Profit & Loss

A shopkeeper gives 12% discount on the marked price and gives two articles free on buying every 14 articles and thus gain 26%. The marked price is above the cost price by

OPtion

1) 54.54%
2) 33.33%
3) 63.63%
4) 36.36%
5) 66.66%
6) 72.72%
7) 48.48%
8) 31.81%
9) 41.66%
10) None of these

Solution

On MP of 14 articles, shopkeeper is giving 12% discount and 2 articles free. Thus on selling 16 articles he is gaining 26%.
⇒ 88% of MP of 14 articles = 126% of CP of 16 srticles
(88/100)*14*MP = (126/100)*16*CP
MP/CP = 18/11
In % MP above CP = [(18-11)/11]x100 = 63.63%
Correct Option 3)

Correct Option: 3 Best Solution (1)

08 Jun 2022 Pipes & Cisterns

With uniform flow, taps A and B can fill the tank in 4 and 3 hours respectively. Tap C can empty the completely filled tank in one and half hour. Tap A is opened at 9:30 am, tap B is opened at 10:15 am and tap C is opened at 11 am. At what exact time will the tank be empty?

OPtion

1) 7:00 pm
2) 6:15 pm
3) 7:30 pm
4) 5:45 pm
5) 6:30 pm
6) 5:00 pm
7) 4:30 pm
8) 6:45 pm
9) 5:30 pm
10) None of these

Solution

Let total capacity of tank be LCM(4, 3, 1.5) = 12 units
Tap A fills 12/4 =3 units per hour.
Tap B fills 12/3=4 units per hour
Tap R empties 12/1.5=8 units per hour.
Upto 11 am, tap A fills for 3/2 hours and B for 3/4 hour .'. Filling upto 11 am = (3/2)x3 + (3/4)x4 = 7.5 units
Now, when each tap is opened together after 11 am, filling per hour 3 + 4 - 8 = -1 units
i.e. 1 unit will be drained per hour, so to empty tank completely it require 7.5 hours after 11 am.
Hence, tank will be completely empty at 6:30 pm

Correct Option: 5 Best Solution (1)

07 Jun 2022 Time Distance & Speed

Arjun can complete a round of a circular track in 72 seconds. Birju, running in opposite direction crosses Arjun at every 18 seconds, then Birju can complete a round of circular track in (sec)

OPtion

1) 30
2) 54
3) 27
4) 24
5) 21
6) 28
7) 16
8) 48
9) 36
10) None of these

Solution

Let t = Birju′s time in seconds to complete 1 round.
Let L represent the length of the track, then speed of Arjun = L/72 and Birju = L/t
We have (L/72)*18 + (L/t)*18 = L
⇒ t=24 sec

Correct Option: 4 Best Solution (1)

06 Jun 2022 Number System

A 10 digit number 7x584805y6 is divisible by 72, then maximum value of √(xy) = ?

OPtion

1) 2√5
2) 2√6
3) 2√3
4) 2√14
5) 3√6
6) 2√7
7) 3√2
8) 4√2
9) √21
10) None of these

Solution

To be divisible by 72 the number must be divisible by 8 and 9 as 8 x 9 = 72
Divisibility rule by 8: The last three digits i.e. unit's, ten's and hundredth digit must be divisible by 8.
Divisibility rule by 9: Sum of digits of number must be divisible by 9 completely.
Let us apply divisibility rule of 8 in a number for last three digits 5y6
5y6 is completely divisible by 8 only when y = 3, 7
Let us put first y=3, then apply the divisibility rule by 9
Sum of the digits = 7+ x + 5 + 8 + 4 + 8 + 0 + 5 + 3 + 6 = x + 46
For the number to be divisible by 9, x=8
Similarly for y=7, checking divisibility rule by 9
Sum of the digits = 7+ x + 5 + 8 + 4 + 8 + 0 + 5 + 7 + 6 = x + 50
For the number to be divisible by 9, x=4
Thus, we have two sets of x,y i.e x=8, y=3 and x=4, y=7
Hence maximum value of √(xy) = √(4*7) = 2√7

Correct Option: 6 Best Solution (0)

03 Jun 2022 Geometry

If x and y are the lengths of two sides of a triangle such that the product xy=18, where x and y are integers, then how many such triangles are possible ?

OPtion

1) 7
2) 10
3) 4
4) 9
5) 5
6) 12
7) 8
8) 6
9) 13
10) None of these

Solution

The length of third side of a triangle must always be between 'Sum and the difference of other two sides '
Let x, y and z are sides of a triangle, where (x-y) < z < (x+y)
Given, product of two sides x and y = xy = 18
Different possible values of (x,y) are (1,18) (2,9) (3,6)
For x=1, y=18 : (18-1) < z < (18+1), z=18
For x=2, y=9 : (9-2) < z < (9+2), z=8, 9, 10
For x=3, y=6 : (6-3) < z < (6+3), z=4, 5, 6, 7, 8
Thus third side z can take 9 different values.
Correct Option 4)

Correct Option: 4 Best Solution (0)

02 Jun 2022 Average

In a class there are total 63 students. The average age of girls is 24 years and that of boys is 21 years. If the average age of whole class is 22 years and 8 months, then number of boys in a class is

OPtion

1) 42
2) 35
3) 36
4) 14
5) 52
6) 48
7) 56
8) 28
9) 44
10) None of these

Solution

Let there be 'x' boys and (63-x) girls in a class.
22 years & 8 months = 22 (8/12) years = 68/3 years
Average age of whole class = [ 21x + (63-x)*24 ] / 63 = 68/3
Solving, we get x=28
.'. Number of boys in a class is 28.

Correct Option: 8 Best Solution (1)

01 Jun 2022 Profit & Loss

A trader bought two articles for Rs. 17,000. He sold one at a profit of 20% and the other at loss of 25%. If the selling price of an article sold at 25% loss is 500/9% of the selling price of an article sold at 20% profit. The gain or loss percentage in the whole transaction is

OPtion

1) 1.17% Gain
2) 2.35% Gain
3) 3.82% Loss
4) 1.77% Loss
5) 3.82% Gain
6) 5.85% Gain
7) 1.17% Loss
8) 2.35% Loss
9) 5.85% Loss
10) None of these

Solution

Let the CP of two articles be Rs. x and Rs. (17000-x) respectively and first article is sold at 20% profit and second at 25% loss.
SP of an article at 20% gain = (120/100)*x
SP of an article at 25% loss = (75/100)*(17000-x)
Then, (75/100)*(17000-x) = (500/9)*(1/100)*(120/100)*x
Solving, we get x=9000
.'. CP of an articles are Rs. 9000 and Rs. 8000
Total SP = (120/100)*9000 + (75/100)*8000 = 16800
Loss = CP - SP = 17000 - 16800 = Rs. 200
% Loss = (200/17000)*100 = 1.17%

Correct Option: 7 Best Solution (0)

31 May 2022 Sequence & Series

Select the letter cluster that can replace the question mark (?) in the given series
BGFZ , FKJU , ? , OSRK , TWVF

OPtion

1) LOPP
2) LPNP
3) JONP
4) JNNP
5) KOOP
6) KNNP
7) LONP
8) KONP
9) KPNP
10) None of these

Solution

Observe the separate letter-wise pattern according to its position in the given series.
1st letters: B, F, ?, O, T ⇒ Letters positioned at 2, 6, __, 15, 20 i.e. with difference of 4, 5, 4, 5, .., so letter at postion 11=K
2nd letters: G, K, ? , S, W ⇒ Letters positioned at 7, 11, __, 19, 23 i.e. with difference of 4, so letter at position 15=O
3rd letters: F, J, ? , R, V ⇒ Letters positioned at 6, 10, __, 18, 22 i.e. with difference of 4, so letter at position 14=N
4th letters: Z, U, ?, K, F ⇒ Letters positioned at 26, 21, __, 11, 6 i.e. with difference of 5 in reverse order, so letter at position 16=P
.'. Required cluster of lettrs is KONP
Correct Option 8)

Correct Option: 8 Best Solution (0)

30 May 2022 Number System

If a + b = 40 and a² + b² = 872, then a³ + b³ = ?

OPtion

1) 8640
2) 2880
3) 11520
4) 10160
5) 28000
6) 20320
7) 15240
8) 40720
9) 19000
10) None of these

Solution

Given, a + b = 40 and a² + b² = 872
(a+b)² = a² + b² + 2ab
40² = 872 + 2ab
⇒ ab = 364
Now, a³ + b³ = (a+b) (a² + b² - ab) = 40*(872 -364) = 20320
Correct Option 6)

Correct Option: 6 Best Solution (1)