M4maths Previous Puzzles

19 Dec 2018 Speed and Distance

Venkateshwara could either walk or drive to office. The time taken to walk to the office is 11 times the driving time. One day, his wife took the car making him walk to office. After walking 1.5 km, he reached a temple when his wife called to say that he can now take the car. Venkateshwara figured that continuing to walk to the office will take as long as walking back home and then driving to the office. Calculate the distance between the temple and the office in KMs.

OPtion

1) 13/10
2) 33/10
3) 9/5
4) 23/10
5) 5/9
6) 17/10
7) 16/10
8) 19/9
9) 21/10
10)None of these

Solution

Suppose the distance between his home and office is x km. Then, distance between his office and temple is (x – 1.5) km.
If he walks at a speed of y km/hr. Then his driving speed = 11y km/hour, as he is 11 times faster in car.

Then,
Time Taken To walk back Home from temple + Time Taken to drive to office from home = Time taken to walk to office from temple
3/2y + x/11y = (x – 3/2)/y
Or, 3 = 10x/11
Or, x = 33/10
Finally, x – 1.5 = 33/10 - 3/2 = (33-15)/10 = 18/10 = 9/5
Option 3)

Correct Option: 3 Best Solution (3)

18 Dec 2018 Area

If the diagonal of a rectangle is 19cm long and its perimeter is 50 cm. Find the area of the rectangle in sq. cm.

OPtion

1) 264
2) 280
3) 140
4) 160
5) 132
6) 144
7) 288
8) 150
9) 130
10) None of these

Solution

Let length = x and breadth = y then

2(x+y) = 50 => x+y = 25
x²+y² = 19² = 361
now (x+y)² = 25²
=> x²+y²+2xy= 625
=> 361 + 2xy = 625
=> xy = 132
area = xy = 132 sq.cm

Option 5)

Correct Option: 5 Best Solution (7)

17 Dec 2018 Simple Interest

At what simple interest rate percent per annum will a sum of money double in 15 years.

OPtion

1) 7.50
2) 6.00
3) 7.33
4) 7.50
5) 7.25
6) 7.14
7) 7.75
8) 6.66
9) 6.75
10) None of these

Solution

SI = PRT/100

SI = P

So P = P*R*15/100
= R= 100/15 = 6.66
Option 8)

Correct Option: 8 Best Solution (8)

14 Dec 2018 Mean, Median and Mode

Find the value of x*y*2*z/5
where x = Mean , y = Median and z = Mode of following numbers:
57 59
56 81 69
55 64
63 81

OPtion

1) 331395
2) 331495
3) 331595
4) 331695
5) 331795
6) 132378
7) 132478
8) 132578
9) 132678
10) None of these

Solution

Mean x = Sum of nos. / Count of numbers = 585/9 = 65 = x
Median y = Middle term when number are arranged in ascending order = 63 = y
Mode z = Number which is present maximum number of times = 81 = z
=> x*y*2*z/5 = 65*63*2*81/5 = 132678


Option 9)

Correct Option: 9 Best Solution (0)

13 Dec 2018 Mixture

A merchant has 640 kg of sugar, part of which he sells at 2% loss and the rest at 6% profit. He gains 3% on the whole. What is the difference between the quantities of sugar sold at 2% loss and that sold at 6% profit?

OPtion

1) 180 kgs
2) 120 kgs
3) 105 kgs
4) 115 kgs
5) 125 kgs
6) 160 kgs
7) 135 kgs
8) 110 kgs
9) 240 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 - 103)/(103-98) = 3/5

Total Quantity = 640 KG

The quantity sold at 2% loss is = (3/8) * 640 = 240 Kgs
The quantity sold at 6% profit is = (5/8) * 640 = 400 Kgs
Difference between Quantity = 400-240 = 160 Kgs


Option 6)

Correct Option: 6 Best Solution (0)

12 Dec 2018 Series

What is the seventh term of following series:
34, 55, 89, 144, 233

OPtion

1) 291
2) 293
3) 377
4) 333
5) 510
6) 590
7) 610
8) 367
9) 387
10) None of these

Solution

Series is formed by Fibonacci numbers starting at 34 and 55 so next number is 144+233 = 377

So seventh term = 233+377 = 610

Option 7)

Correct Option: 7 Best Solution (2)

11 Dec 2018 Probability

A prime number number less than 50 is randomly picked, what is probability that one of its digit will be 1?

OPtion

1) 1/4
2) 5/16
3) 5/14
4) 3/7
5) 2/5
6) 1/3
7) 7/15
8) 7/13
9) 6/13
10) None of these

Solution

Total number of prime numbers less than 50 = 15 => 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47
Number of positive outcomes i.e. number where at least one of its digit is 1 = 6

Probability = 6/15 = 2/5

Correct Option: 5 Best Solution (0)

10 Dec 2018 Interest

There is 60% increase in an amount in 5 years at simple interest. What will be the compound interest of Rs. 10,000 after 3 years at the same rate (compounded annually)?

OPtion

1) 4149.28
2) 4049.28
3) 4949.28
4) 4249.28
5) 4349.28
6) 4449.28
7) 4549.28
8) 4649.28
9) 4749.28
10) None of these

Solution

Let P be Rs 100 then SI after 5 years is Rs. 60

R = (SI/P*T) *100 = (60/100*5)*100 = 12%


CI = A{[ 1+ R/100]^T - 1 }
=> 10000 { [ 1 + 12/100]^3 - 1}
=> 10000 { [112/100]^3 - 1} = 4049.28
Option 2)

Correct Option: 2 Best Solution (9)

07 Dec 2018 Area

Given hypotenuse of a right angled triangle ABC is 17cm and its base is 15cm, what is the area of triangle ABC in cm^2?

OPtion

1) 60
2) 30
3) 120
4) 40
5) 25
6) 90
7) 50
8) 80
9) 10
10) None of these

Solution

B= 15, H=17 and L =?

L^2 + B^2 = H^2
=> L^2 = H^2 - B^2 = 17^2 - 15^2 = 64
=> L = 8

Area of triangle = 8*15/2 = 60cm^2

Correct Option: 1 Best Solution (2)

06 Dec 2018 Probability

If a letter is randomly taken from the word OCTOPUS, what is the probability that it would be a vowel?

OPtion

1) 2/7
2) 1/7
3) 4/7
4) 1/5
5) 1/8
6) 3/8
7) 13/70
8) 3/7
9) 2/9
10) None of these

Solution

Total Number of chacraccters in OCTOPUS = 7
Number of VOWELS 2 Os and 1 U= 3

Probability = 3/7

Correct Option: 8 Best Solution (2)