M4maths Previous Puzzles

17 Jan 2018 Percentage

If Rs.75000 is to be divided among Amar, Akbar and Anthony so that Amar receives 10% more than Akbar and Akbar receives 10% less than Anthony, then Amar's shares is

OPtion

1) Rs.23356.40
2) Rs.25951.50
3) Rs.25962.04
4) Rs.27951.05
5) Rs.25692.04
6) Rs.25591.50
7) Rs.25992.40
8) Rs.26692.04
9) Rs.25552.87
10) None of these

Solution

Suppose Anthony's gets Rs.100 then Akbar gets Rs.90
Amar gets = 10% more than Akbar = 90*110/100 = 99

Aamr:Akbar:Anthony = 99:90:100

Therefore Aamr's share = (99/289)*75000 = Rs. 25692.04
Option 5)

Correct Option: 5 Best Solution (0)

16 Jan 2018 Ratio

Eena, Meena and Deeka start a spa with their investment ratio of 4:7:8. Eena withdraws her investment after 6 month. If profit is distributed between them yearly, then ratio of profit of Deeka and profit of Eena in the business is

OPtion

1) 7:8
2) 7:2
3) 8:1
4) 1:4
5) 1:8
6) 4:1
7) 8:7
8) 4:3
9) 1:6
10)6:1

Solution

The effective proportion of Eena= 4 * 6 (month) = 96
the effective proportion of Meena = 7 * 12 (month)
And the effective proportion of Deeka = 8 * 12 (month)
Hence Ratio of Deeka : Eena = 8*12 : 4*6 = 4:1

Option 6)

Correct Option: 6 Best Solution (3)

15 Jan 2018 Series

Find the 8th term of following series:
02, 13, 15, 27, 311, 513,...

OPtion

1) 615
2) 713
3) 815
4) 819
5) 717
6) 813
7) 1319
8) 817
9) 1317
10) None of these

Solution

nth term of series is formed by concatenation of nth term of Fibonacci series and nth term of prime number
So 8th term of Fibonacci series is 13
And 8th prime number is 19

So Answer is 1319

Correct Option: 7 Best Solution (0)

12 Jan 2018 Profit and Loss

Robert buys an old scooter for Rs. 23450 and spends Rs. 1850 on its repairs. If he sells the scooter for Rs. 29500, his gain percent is:

OPtion

1) 15.58 %
2) 16.06 %
3) 17.48 %
4) 15.85 %
5) 16.90 %
6) 16.60 %
7) 17.80 %
8) 17.30 %
9) 15.95 %
10) None of these

Solution

Cost Price (C.P.) = Rs. (23450 + 1850) = Rs. 25300

Selling Price (S.P.) = Rs. 29500

Gain = (S.P.) - (C.P.) = Rs.(29500 - 25300) = Rs. 4200

Gain % = (4200/25300)*100 = 16.60 %

Option 6)

Correct Option: 6 Best Solution (6)

11 Jan 2018 Area

The length, breadth and height of a room are in the ratio 9:7:5. If the breadth and length are doubled while the height is halved. Then the total area of the 4 walls of the room will:

OPtion

1) Increase by 10%
2) Increase by 22%
3) Increase by 25%
4) Increase by 15%
5) Increase by 7%
6) Increase by 20%
7) Increase by 9%
8) Increase by 0%
9) Increase by 8%
10)None of these

Solution

l:b:h=9:7:5


Area of 4 walls = 2*(l+b)*h

Inital Area:
Let h=5x, b=7x and l=9x
Area of 4 walls = 2*(9x+7x)*5x = 160x^2

New dimensions when the breadth and length are doubled while the height is halved
l1=18x
b1=14x
h1=2.5x

New Area
Area2= 2*(18x+14x)* 5x/2x = 160x^2
% Increase in area = (160-160)*100/160 = 0%

Option 8)

Correct Option: 8 Best Solution (8)

10 Jan 2018 Sum of Digits

Find sum of all the 3 digit number formed by using digits 2, 5, 7 & 9 (repetition being not allowed).

OPtion

1) 14112
2) 15246
3) 13860
4) 12466
5) 13986
6) 15600
7) 12726
8) 14238
9) 12978
10)None of these

Solution

Total combination are
{2,5,7}, {2,5,9}, {2,7,9} and {5,7,9}

2*(13)*111+2*15*111+ 2*17*111 + 2*18*111

In every set of 3 numbers, 6 arrangements are possible - with each digit being 2 times at hundred place, 2 times at tens place and 2 times at units place. For example in case of {2,5,7} = 257, 275, 527, 572, 725, 752

So Sum of all numbers formed from set {2,5,7} = 2*(2+5+7)*100 + 2*(2+5+7)*10 + 2*(2+5+7)*1 = 3108
Similarly,
Sum of all numbers formed from set {2,5,9} = 2*(2+5+9)*100 + 2*(2+5+9)*10 + 2*(2+5+9)*1 = 3552
Sum of all numbers formed from set {2,7,9} = 2*(2+7+9)*100 + 2*(2+7+9)*10 + 2*(2+7+9)*1 = 3996
Sum of all numbers formed from set {5,7,9} = 2*(5+7+9)*100 + 2*(5+7+9)*10 + 2*(5+7+9)*1 = 4662

Sum of all = 15318

Correct Option: 10 Best Solution (1)

09 Jan 2018 Distance

Two ships are sailing in the sea on the two sides of a lighthouse. The angle of elevation of the top of the lighthouse is observed from the ships are 30° and 30° respectively. If the lighthouse is 69 m high, the distance between the two ships is:

OPtion

1) 231.02 m
2) 232.02 m
3) 233.02 m
4) 234.02 m
5) 235.02 m
6) 236.02 m
7) 237.02 m
8) 238.02 m
9) 239.02 m
10)None of these

Solution

Let AB be the lighthouse where A is the bottom point of light house and C and D be the positions of the ships.
Then, AB = 69 m, Angle ACB = 30° and angle ADB = 30°.
AB/AC = tan 30° = 1/3^(1/2)
=> AC = AB * 3^(1/2) = 69*3^(1/2)

AB/AD = tan 30° = 1/3^(1/2)
=> AD = AB*3^(1/2) = 69*3^(1/2)

CD = (AC + AD) = 69*3^(1/2) + 69*3^(1/2)
= 239.02

Option 9)

Correct Option: 9 Best Solution (14)

08 Jan 2018 Percentage

Padnya scored 93 runs in 95 balls in 1st innings of cape town test match against South Africa which included fourteen fours and one six. What percent of his total 1st innings score did he make by running between the wickets?

OPtion

1) 25.12%
2) 30.00%
3) 35.50%
4) 29.82%
5) 33.66%
6) 30.33%
7) 29.33%
8) 33.33%
9) 22.22%
10)None of these

Solution

Number of runs made by running = 93 - ((14 x 4) + (1 x 6))
= 93 - (62) = 31

Required percentage = (31/93)*100 = 33.33%
Option 8)

Correct Option: 8 Best Solution (3)

05 Jan 2018 Direction Sense

Tony started from his house towards west. After covering a distance of 9.5 km. he turned towards left and covered a distance of 6 km. Then he turns right and covers a distance of 4.5 . What is the shortest distance now from his house?

OPtion

1) 15.91
2) 7.81
3) 16.23
4) 16.29
5) 14.31
6) 14.81.
7) 15.23
8) 14.81
9) 7.18
10) None of these

Solution

As per question Tony starts from Point A and moves to Point B in west by travelling 9.5 KM. Then he turns left and travels 6KM to reach point C. Then he turns right and travels 4.5 KMs to reach point D. We need to find shortest distance between D and A

9.5
B-------------A
|
| 6
|
C------D
4.5

Horizontal distance between AD = 9.5+4.5 =14
Vertical distance between AD = 6
We need to find shortest distance between A and D = Sq. root (14^2 + 6^2 ) = ~15.23 KMS

Correct Option: 7 Best Solution (0)

04 Jan 2018 Profit and Loss

720 bananas are bought for Rs. 2520 and sold at the rate of Rs. 58 per dozen. The percentage of profit or loss is:

OPtion

1) 30 % Profit
2) 3.333 % Profit
3) 33.333 % Profit
4) 35.555 % Profit
5) 36.6666 % Profit
6) 37.7777 % Profit
7) 31.111 % Profit
8) 32.222 % Profit
9) 34.5 % Profit
10) None of these

Solution

Cost of 1 banana= 2520/720 = 3.5
Selling price of 1 banana = 58/12 = Rs. 4.83333

As SP > CP so its profit
So Profit % = (4.66667 - 3.5 )*100/3.5 = 38.09 %
Option 10)

Correct Option: 10 Best Solution (0)