M4maths Previous Puzzles

24 May 2017 Decode

If
16+24 = 12,
36+54 = 27 and
20+60 = 25

Then what is the value of:
28+72 = ?

OPtion

1) 14
2) 21
3) 31
4) 37
5) 33
6) 27
7) 36
8) 30
9) 35
10) None of these

Solution

16+24 = 4*(4) + 3*(8) = 4+8 = 12,
36+54 = 4*(9) + 3*18()= 9+18 = 27 and
20+60 = 4*(5) + 3*(20) = 5+20 = 25

Similarly 28+72 = 4*(7) + 3*(24) = 7+24 = 31
Option 3)

Correct Option: 3 Best Solution (8)

23 May 2017 Clock

An accurate clock shows 7 o'clock in the morning. Through how may degrees will the hour hand rotate when the clock shows 2:30 in the afternoon?

OPtion

1) 215 degree
2) 150 degree
3) 240 degree
4) 210 degree
5) 225 degree
6) 200 degree
7) 205 degree
8) 175 degree
9) 185 degree
10) None of these

Solution

We know that angle traced by hour hand in 12 hrs = 360°

From 7 to 2:30, there are 7.5 hours.

Angle traced by the hour hand in 7.5 hours = 7.5×360/12
=225 degree

Correct Option: 5 Best Solution (20)

22 May 2017 Profit and Loss

When an item is sold for Rs. 26,100, the owner loses 13%. At what price should that plot be sold to get a gain of 13.5 % ?

OPtion

1) 38600
2) 35000
3) 33900
4) 30000
5) 36000
6) 32600
7) 34050
8) 34900
9) 36900
10) None of these

Solution

When the item is sold for Rs. 26,100, loss is 13%
So cost price = 26,100 * 100/87 = 30,000

To gain 13.5% selling price = 113.5*30,000/100 = 34,050

Correct Option: 7 Best Solution (20)

19 May 2017 Root and Power

If 4^(n + 4) - 4^(n + 2) = 960, What is the value of n?

OPtion

1) 0
2) 3
3) 4
4) 1
5) -1
6) 2
7) -3
8) -2
9) -4
10) None of these

Solution

4^(n + 4) - 4^(n + 2) = 960

=> 4^(n + 2 + 2) - 4^(n + 2) = 960

=> 4^(n + 2) × 4^(2) - 4^(n + 2) = 960

=> 4^(n + 2)[4^(2) - 1] = 960

=> 4^(n + 2) × (15) = 960

=> 4^(n + 2) = 64
4^(n + 2) = 4^3
=> n + 2 = 3
=> n = 1

Correct Option: 4 Best Solution (7)

18 May 2017 Radius and Volume

11 solid spheres of radius 3 m, 9 solid cylinder of radius 4 m, height 5 meter and 13 solid cones of radius 2 m, height 4 m are melted to form a bigger solid sphere. What is the radius of this bigger solid sphere in meters?

OPtion

1) 9.22
2) 10.02
3) 9.62
4) 8.98
5) 9.89
6) 10.09
7) 8.79
8) 10.04
9) 8.62
10)None of these

Solution

Volume of 11 smaller sphere's = 11*(4/3)*Pi*r1^3
Volume of 9 Cylinder = 9*(Pi*r2^2*h1)
Volume of 13 Cones = 13*(1/3)*Pi*r3^2*h2
Volume of Larger Sphere = (4/3)*Pi*R^3

Here r1=3m, r2=4m, r3=2m, h1=5m, h2=4m, and R=?
Volume of Larger Sphere = Volume of 11 smaller sphere's + Volume of 9 Cylinder +Volume of 13 Cones
=> (4/3)*Pi*R^3 = 11*(4/3)*Pi*r1^3 + 9*P1*r2^2*h1 + 13*(1/3)*Pi*r3^2*h2

=> 4/3*R^3 = 4*99 + 9*80 + 13*16/3 = 1185.333
=> R^3 = 889
R = 889^(1/3) = 9.62 m

Option 3)

Correct Option: 3 Best Solution (7)

17 May 2017 Trains

Two trains each 365 meter long, are running in same directions on parallel tracks. If their speeds are 44 km/hr and 64 km/hr respectively, the time taken by the faster train to pass the driver of the slower one is?

OPtion

1) 12.55 seconds
2) 12.31 seconds
3) 12.93 seconds
4) 12.00 seconds
5) 12.16 seconds
6) 63.50 seconds
7) 64.26 seconds
8) 66.30 seconds
9) 64.01 seconds
10) None of these

Solution

Relative speed= 64-44 = 20 km/hr = 20 * 5/18 = 50/9 m/sec

We are calculating the time taken by the faster train to pass the driver of the slower one.
Hence, distance = length of the faster train = 365 metre

Time = 365/50/9 = 65.7 seconds

Option 10)

Correct Option: 10 Best Solution (10)

16 May 2017 Mixture

A merchant has 144 kg of sugar, part of which he sells at 3% loss and the rest at 9% profit. He gains 5% on the whole. What is the quantity of sugar sold at 3% loss?

OPtion

1) 96 kg
2) 90 kg
3) 100 kg
4) 72 kg
5) 60 kg
6) 50 kg
7) 45 kg
8) 48 kg
9) 84 kg
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) = (109 - 105)/(105-97) = 4/8 = 1/2

Total Quantity = 144 KG

The quantity sold at 3% loss is = (1/3) * 144 = 48 Kgs

Option 8)

Correct Option: 8 Best Solution (12)

15 May 2017 Simple Interest

A sum of money at simple interest amounts to Rs. 483 in 3 years and to Rs. 504 in 4 years. The sum is:

OPtion

1) Rs. 400
2) Rs. 350
3) Rs. 375
4) Rs. 300
5) Rs. 250
6) Rs. 420
7) Rs. 440
8) Rs. 450
9) Rs. 500
10) None of these

Solution

S.I. for 1 year = Rs. (504 - 483) = Rs. 21

S.I. for 3 years = Rs.(21 x 3) = Rs. 63

Principal = Rs. (483 - 63) = Rs. 420

Correct Option: 6 Best Solution (17)

12 May 2017 Probability

What is the probability of getting a sum of 5 in a toss of a pair of dice?

OPtion

1) 4/13
2) 2/36
3) 8/36
4) 4/35
5) 7/36
6) 5/36
7) 1/6
8) 1/9
9) 5/18
10) None of these

Solution

Total number of outcomes= 36
Total Number of positive outcomes = (1,4) (4,1) (2,3) (3,2) = 4

Probability = 4/36 = 1/9

Correct Option: 8 Best Solution (10)

11 May 2017 Profit and Loss

600 banana's are bought for Rs. 720 and sold at the rate of Rs. 15 per dozen. The percentage of profit or loss is:

OPtion

1) 2.8% Profit
2) 4.16% Profit
3) 2.8% Loss
4) 4.16% Loss
5) 2.0% Loss
6) 5.8% Profit
7) 5.2% Profit
8) 4.5% Profit
9) 3.0% Profit
10) None of these

Solution

Cost of 1 banana = 720/60 = 1.2
Selling price of 1 banana = 15/12 = Rs. 1.25

As SP > CP so its profit
So Profit % = (1.25 - 1.2)*100/1.2 = 4.16%
Option 2)

Correct Option: 2 Best Solution (23)