M4maths Previous Puzzles

06 Jun 2018 Mixture

A merchant has 550 kg of sugar, part of which he sells at 4% loss and the rest at 6% profit. He gains 2% on the whole. What is the difference between the quantities of sugar sold at 6% profit and that sold at 4% loss?

OPtion

1) 93 kgs
2) 120 kgs
3) 105 kgs
4) 115 kgs
5) 125 kgs
6) 130 kgs
7) 135 kgs
8) 110 kgs
9) 220 kgs
10)None of these

Solution

(Quantity of Cheaper)/(Quantity of Dearer) = (Price of Dearer - Mean Price)/(Mean Price - Price of Cheaper)

(Quantity of Cheaper)/(Quantity of Dearer) = (106 - 102)/(102-96) = 4/6 = 2/3

Total Quantity = 550 KG

The quantity sold at 4% loss is = (2/5) * 550 = 220 Kgs
The quantity sold at 6% profit is = (3/5) * 550 = 330 Kgs
Difference between Quantity = 330-220 = 110 Kgs


Option 8)

Correct Option: 8 Best Solution (5)

05 Jun 2018 Probability

A prime number less than 60 is randomly picked, what is probability that one of its digit will be 2?

OPtion

1) 1/5
2) 3/16
3) 2/17
4) 3/17
5) 1/8
6) 1/7
7) 3/18
8) 2/13
9) 1/17
10) None of these

Solution

Total number of prime numbers less than 60 = 17 => 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59
Number of positive outcomes i.e. number where at least one of its digit is 2 = 3

Probability = 3/17

Correct Option: 4 Best Solution (4)

04 Jun 2018 Age

In 2017, A is 9 years older than B who is five times as old as C. The total of the ages of A, B and C is 97 years. What would be the average of A and C ages in the year 2024 ?

OPtion

1) 31 years
2) 30 years
3) 33 years
4) 34.5 years
5) 36.5 years
6) 35.5 years
7) 29 years
8) 24 years
9) 35 years
10)None of these

Solution

Let’s assume Age of B be B years
Age of A = B+9
Age of C = B/5

Total age = B + 9 + B + B/5 = 97
Solving 11B/5 = 88
B = 40
A = B+9 = 40+9 = 49
C = 40/5 = 8

Age of A in 2024 = 49+7 = 56
Age of C in 2024 = 8+7 = 15

Average of ages in 2024 = (56+15)/2 = 35.5

Option 6)

Correct Option: 6 Best Solution (0)

01 Jun 2018 Time and Work

P can do a work in 46.5 days. Q can do the same work in 31 days and R can do the same in 77.5 days. Q and R start the work and leave after 15 days. P finishes the remaining work in X days. What is the value of X?

OPtion

1) 20.0 days
2) 16 days
3) 17 days
4) 12 days
5) 13 days
6) 15 days
7) 14 days
8) 11 days
9) 18 days
10) None of these

Solution

Amount of work done by Q and R in 15 days = 15*(1/31 + 1/77.5) = 15((2.5+1)/77.5) = 52.5/77.5 = 21/31
Amount of work remaining after 15 days = 10/31

Amount of work done by P in 1 day = 1/46.5
So for 1/46.5 work P takes 1 day
Hence for 10/31 work P would take (1/(1/46.5))*10/31 = 15 days

Option 6)

Correct Option: 6 Best Solution (5)

31 May 2018 LCM

Two numbers are in the ratio 3 : 5. If their L.C.M. is 210. what is product of the numbers?

OPtion

1) 2940
2) 2730
3) 2960
4) 2715
5) 3110
6) 2907
7) 2840
8) 2870
9) 2890
10) None of these

Solution

Let the numbers be 3x and 5x
LCM of 3x and 5x is 15x

So as per question 15x = 210
=> x= 14

3x = 42 and 5x = 70

Product = 2940

Option 1)

Correct Option: 1 Best Solution (6)

30 May 2018 Profit and Loss

Robert buys an old scooter for Rs. 22500 and spends Rs. 3500 on its repairs. If he sells the scooter for Rs. 32500, his gain percent is:

OPtion

1) 27.02 %
2) 25.82 %
3) 26.09 %
4) 24.05 %
5) 27.92 %
6) 25.00 %
7) 23.80 %
8) 26.30 %
9) 27.52 %
10) None of these

Solution

Actual CP for Robert = 22500 + 3500 = 26000
SP = 32500

Profit = (32500 - 26000)/26000 = 25%

Correct Option: 6 Best Solution (5)

29 May 2018 Age

In 2017, A is 6 years older than B who is seven times as old as C. The total of the ages of A, B and C is 126 years. What would be the average of A and B ages in the year 2029 ?

OPtion

1) 44 years
2) 47 years
3) 71 years
4) 69 years
5) 42 years
6) 40 years
7) 73 years
8) 72 years
9) 75 years
10)None of these

Solution

Let’s assume Age of B be B years
Age of A = B+6
Age of C = B/7

Total age = B + 6 + B + B/7 = 126
Solving 15B/7 = 120
B = 56
A = B+6 = 62
C = 56/7 = 8

Age of A in 2029 = 62+12 = 74
Age of B in 2029 = 56+12 = 68

Average of ages in 2029 = (74+68)/2 = 71

Option 3)

Correct Option: 3 Best Solution (3)

28 May 2018 Series

Find the eleventh term
3, 4, 6, 8, 12, 14, 18, 20, 24, 30, ....

OPtion

1) 28
2) 32
3) 34
4) 36
5) 38
6) 30
7) 26
8) 40
9) 42
10) None of these

Solution

Series is formed by prime numbers + 1
2+1=3
3+1=4
5+1=6
7+1=8
11+1=12
13+1=14
17+1=18
19+1=20
23+1=24
29+1 =30
31+1 =32

Correct Option: 2 Best Solution (3)

25 May 2018 Age

Sum of the ages of a boy and his father is 49 years. Before 11 years Father's age was 8 times the age of the boy. What was the age of father (in years) at the time of birth of the child?

OPtion

1) 20
2) 22
3) 23
4) 21
5) 24
6) 28
7) 25
8) 26
9) 27
10) None of these

Solution

Sum of current ages = 49

11 years back
Sum of Ages = 49-11*2 =27 years

11 years back if age of son is x then fathers age is = 8x

so x+8x =27
=> x = 3
=> 8x = 24

At the time of birth of son, age of father = 24-3 = 21 years

Correct Option: 4 Best Solution (0)

24 May 2018 LCM

Two numbers are in the ratio 3 : 4. If their L.C.M. is 192. what is product of the numbers?

OPtion

1) 3072
2) 2884
3) 2928
4) 3216
5) 2784
6) 3084
7) 3060
8) 2796
9) 3204
10) None of these

Solution

Let the numbers be 3x and 4x
LCM of 3x and 4x is 12x
So as per question 12x = 192
=> x= 16

3x = 3*16 = 48 and 4*16 = 64
Product of the numbers = 3072

Correct Option: 1 Best Solution (0)