M4maths Previous Puzzles

24 Apr 2019 Area

If the diagonal of a rectangle is 18cm long and its perimeter is 44 cm. Find the area of the rectangle.

OPtion

1) 70 sq.cm
2) 76 sq.cm
3) 78 sq.cm
4) 74 sq.cm
5) 75 sq.cm
6) 72 sq.cm
7) 80 sq.cm
8) 86 sq.cm
9) 94 sq.cm
10) None of these

Solution

Let length = x and breadth = y then

2(x+y) = 44 => x+y = 22
x²+y² = 18² = 324
now (x+y)² = 22²
=> x²+y²+2xy= 484
=> 324 + 2xy = 484
=> xy = 80

Area = xy = 80 sq.cm

Correct Option: 7 Best Solution (5)

23 Apr 2019 Series

What is the next term of following series:
1, 2, 4, 6, 10, 12, 16, ?

OPtion

1) 19
2) 18
3) 20
4) 21
5) 23
6) 22
7) 24
8) 25
9) 26
10) None of these

Solution

nth term = n - 1
Where n is prime number such as 2, 3, 5, 7, 11, 13, 17, 19 and so on
So next term = 19 - 1 = 18

Option 2)

Correct Option: 2 Best Solution (0)

22 Apr 2019 Age

The present age of a brother is 7 years more than three times the age of his sister. Nine years hence, brother’s age will be 6 years more than twice the age of the sister. Find the present age of the brother.

OPtion

1) 18
2) 22
3) 30
4) 31
5) 27
6) 24
7) 21
8) 28
9) 32
10) None of these

Solution

Let the sister’s present age be ‘n’ years.
=> brother’s present age = (3n + 7) years
So, according to the question
(3n + 7 + 9) = 2 (n + 9) + 6
=> 3n + 16 = 3n + 24
=> n = 8
Hence, brother’s present age = (3n + 7) = 31 years

Correct Option: 4 Best Solution (5)

19 Apr 2019 Boats and Streams

A man goes down stream with a boat to some destination and returns upstream to his original place in 8 hours. If the speed of the boat in still water and downstream are 12km/hr and 15km/hr respectively, the distance of the destination from the starting place in KMs is

OPtion

1) 48
2) 45
3) 50
4) 46
5) 47
6) 49
7) 44
8) 40
9) 42
10) None of these

Solution

Let the distance be D

Speed of boat in still water = 12
Speed of boat in down stream = 15
Speed of Stream = 15- 12 = 3
Speed of boat in upstream = 12-3 = 9

Time Downstream + Time upstream = 8
=> D/15 + D/9 = 15
=> D = 45
Option 2)

Correct Option: 2 Best Solution (0)

18 Apr 2019 Simple Interest

Divide Rs. 21411 into 3 parts so that their amount after 2,3 and 4 years respectively may be equal, the rate of interest being 5% per annum at simple interest. The second part is

OPtion

1) 8197
2) 6831
3) 7452
4) 7128
5) 6830
6) 7450
7) 7132
8) 6833
9) 7130
10) None of these

Solution

Let the parts be x, y and z
x + (x * 2 * 5/100) = y + (y * 3 * 5/100) = z + (z * 4 * 5/100)
11x/10 = 23y/20 = 6z/5 = k
x = 10k/11, y = 20k/23, z = 5k/6
But x + y + z = 21411
10k/11 + 20k/23 + 5k/6 = 21411
k = 8197.2
y= (20/23)*8197.2 = 7128
Option 4)

Correct Option: 4 Best Solution (2)

17 Apr 2019 Race

In a race of 500 m, A can beat B by 80 m and C by 20 m. In a race of 700 m, C will beat B by:

OPtion

1) 60.0
2) 25.5
3) 85.0
4) 100.0
5) 77.5
6) 82.5
7) 50.5
8) 87.5
9) 75.0
10) None of these

Solution

When A covers 500m B Covers 420m
When A Covers 500m C covers 480m

A : B = 500 : 420
A : C = 500 : 480

C/B = (C/A*A/B) = (480/470) = 480:420
When C covers 480 m, B covers 420 m.
When C covers 700 m, B covers (420/480)*1200)m = 612.5
Therefore, C beats B by (700 - 612.5) m = 87.5 m.

Option 8)

Correct Option: 8 Best Solution (5)

16 Apr 2019 Series

What is the next term of following series:
113, 127, 131, 137, 139

OPtion

1) 141
2) 144
3) 143
4) 145
5) 149
6) 146
7) 147
8) 148
9) 140
10) None of these

Solution

Series is formed by prime number starting at 113 so next prime number is 149
Option 5)

Correct Option: 5 Best Solution (5)

15 Apr 2019 Cost Price

Jallaluddin went to buy 5 chocolates worth Rs. x. He gave Rs.200 rupee note to the shopkeeper to buy the chocolates then shopkeeper gave rest of the money in the denominations of 50 paise, 2 rupee, and 10 rupees. If the ratio of the number of coins is 18:13:9 respectively. Then what is the price of two chocolate?

OPtion

1) 75
2) 12
3) 10
4) 7.5
5) 50
6) 30
7) 15
8) 45
9) 60
10) None of these

Solution

Possible coins = (18, 13, 9) & (36, 26, 18)
If (18, 13, 9) = 0.50*18+ 2*13 + 10*9 =125

Chocolate cost =200 - 125 = 75 Rs

Case 2: (36, 26, 18) = 0.50*26+ 2*26 + 10*18 = 250 which is more than 200 rupees so wrong

So cost of 5 chocolates = Rs 75

Cost of 2 Chocolates = (75/5)*2 = Rs 30
Option 6)

Correct Option: 6 Best Solution (0)

12 Apr 2019 Perfect Square

How many factors of 587042640 are perfect squares?

OPtion

1) 24
2) 20
3) 12
4) 16
5) 18
6) 9
7) 27
8) 30
9) 20
10) None of these

Solution

587042640 = 73^2 * 17^1 * 5^1 * 3^4 * 2^4

Any factor of this number should be of the form 73^a * 17^b * 5^c * 3^d * 2^e

For the factor to be a perfect square a,b,c,d,e have to be even.

a can take values 0,2
b can take values 0,
c can take values 0,
d can take values 0, 2, 4
and e can take values 0, 2, 4


Total number of perfect squares = 2*1*1*3*3 = 18


Option 5)

Correct Option: 5 Best Solution (0)

11 Apr 2019 Ages

The age difference between two brothers is 6 years. After 6 years the ratio between the age is 8:5
What would be the sum of their present ages?

OPtion

1) 11
2) 22
3) 27
4) 33
5) 30
6) 18
7) 15
8) 21
9) 24
10) None of these

Solution

Let a = the age of the younger brother now
a+6 = the age of the older brother now
given:
In 6 years:
a+6 = the age of the younger brother
a+6+6 = the age of the older brother

(a+12)/(a+6)=8/5
=> 5a + 60 = 8a + 48
=> 3a = 12
=> a = 4
=> a+6=10

Sum = 10+4 = 14

Correct Option: 10 Best Solution (4)