M4maths Previous Puzzles

29 Jun 2016 How many unit of work?

If A men working A hours a day can do A units of a work in A days, then B men working B hours per day would be able to complete, how many units of work?

OPtion

1) A^2/B^3
2) A/B^2
3) B^2/A^3
4) A/B^3
5) B^3/A^2
6) B/A^2
7) A^3/B^2
8) B/A^3
9) A/B
10)None of these

Solution

More men, more units (Direct)
More working hours, more units (Direct)
More days, more units (Direct)
Men ------------ A:B
Working hrs ---- A:B --- :: A:P
Days ----------- A:B

=> A*A*A*P=B*B*B*A
So P = B^3/A^2 Units
Option 5)

Correct Option: 5 Best Solution (4)

28 Jun 2016 Rate of interest

A banker paid Rs.5767.50 for a bill of Rs.5840, drawn on April 4, at 6 months. On what day was the bill discounted, the rate of interest being 7%?

OPtion

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

Solution

B.D. = Rs.(5840 - 5767.20) = Rs.72.80
=> Rs.72.80 is S.I. on Rs.5840 at 7%
So unexpired time = 100*72.80 / 7*5840 years = 13/73 = 65 days
Now, date of draw of bill = April, 4 at 6 months
Nominally due date = October, 4
Legally due date = October, 7
So, we must go back 65 days from October, 7
Oct. Sept. Aug.
7+ 30+ 28
i.e., The bill was discounted on 3rd August.

Correct Option: 8 Best Solution (5)

27 Jun 2016 Sequence

What is the missing number.
802, 786, 744, ....., 674, 650

OPtion

1) 710
2) 714
3) 726
4) 718
5) 722
6) 716
7) 736
8) 728
9) 732
10)None of these

Solution

802
802 - (8*2) = 802-16 = 786 (Number - (last*first)number)
786 - (7*6) = 786-42 = 744
=> 744 - (7*4) = 744-28 = 716 <=
716 - (7*6) = 716-42 = 674
674 - (6*4) = 674-24 = 650

Option 6)

Correct Option: 6 Best Solution (21)

24 Jun 2016 Time and distance

A boat covers 24 km upstream and 36 km downstream in 6 hours, while it covers 36 km upstream and 24 km downstream is 13/2 hours. The velocity of the current (in km/hr) is.

OPtion

1) 1
2) 2
3) 1.5
4) 2.5
5) 3
6) 4
7) 3.5
8) 4.5
9) 5
10)None of these

Solution

Let speed upstream & speed downstream be x km/hr and y km/hr respectively. Then
24/x + 36/y = 6 and 36/x + 24/y = 13/2
=> 24u + 36v = 6 and 36u + 24v = 13/2 (u = 1/x and v = 1/y)
Adding we get
u = 1/8 and v = 1/2
=> x = 8 and y = 12
Velocity of current = 1/2 (12-8) km/hr = 2 km/hr

Option 2)

Correct Option: 2 Best Solution (6)

23 Jun 2016 Area

The area of a rectangle is thrice that of a square. Length of the rectangle is 40 cm and the breadth of the rectangle is 3/2 times that of the side of the square. The side of the square in cm is

OPtion

1) 10
2) 15
3) 20
4) 25
5) 30
6) 35
7) 40
8) 50
9) 60
10)None of these

Solution

Let the side of the square be x cm. Then,
40* 3/2 x = 3x^2
or
x = 20
So, side of the sq = 20 cm
Option 3)

Correct Option: 3 Best Solution (9)

22 Jun 2016 Mixture

A lump of two metals weighing 18 gms. is worth Rs.87 but if their weight be interchanged, it would be worth Rs.78.60. If the price of one metal be Rs.6.70 per gm., find the weight of the other metal in the mixture.

OPtion

1) 5 gm
2) 4 gm
3) 8 gm
4) 6 gm
5) 14 gm
6) 12 gm
7) 7 gm
8) 10 gm
9) 9 gm
10)None of these

Solution

If one lump is mixed with another lump with the quantities of metals interchanged then the mixture of the two lumps would contain 18 gm. of first metal and 18 gm. of second metal and the price of the mixture would be Rs. (87+78.60) or Rs. 165.60
=> Cost of (18 gm of 1st metal + 18 gm of 2nd metal)
= Rs. 168.60
So cost of (1 gm of 1st metal + 1 gm of 2nd metal)
= Rs. 165.60/18 = Rs. 9.20
Now mean price of lump = Rs. (87/18) per gm = Rs. (29/6)
By alligation rule
Quantity of 1st metal/Quantity of 2nd metal = 14/6 : 56/30 = 5:4
In 9 gm of mix, 2nd metal = 4 gm
In 18 gm of mix 2nd metal = 4/9 *18 = 8 gm
Option 3)

Correct Option: 3 Best Solution (11)

21 Jun 2016 Amount of the bill?

A bill falls due in 9 months. The creditor agree to accept immediate payment of half and to defer the payment of the other half for 18 months. He finds that by this arrangement he gains Rs.4.50. What is the amount of the bill, if money be worth 4%.

OPtion

1) 20600
2) 20100
3) 10200
4) 10500
5) 10900
6) 10100
7) 10800
8) 10300
9) 20300
10)None of these

Solution

Let the amount of bill be Rs.200. Then, according to the agreement, the creditor agree to pay after 9 month, an amount which is the sum of the amount of Rs. 100 for 9 months and P.W. of Rs. 100 due 9 months hence.
Now, S.I. = Rs.(100*3*4 / 4*100) = Rs.3
=> Amount = Rs.(100+3) = Rs.103
Also, P.W. = Rs.(100*100 / (100+(4* 3/4) = Rs.(10000/103)
Total amount after 9 months = Rs.(103 + 10000/103) = Rs. 20609/103
Gain = Rs.(20609/103 - 200) = Rs.(9/103)
If gain is Rs.(9/103), sum due = Rs.200
If gain is Rs.9/2, Sum due = Rs.(200*103*9 / 9*2) = Rs.10300

Correct Option: 8 Best Solution (0)

20 Jun 2016 Sequence

What is the next number of the following sequence.
69, 93, 108, 125, .......

OPtion

1) 142
2) 139
3) 133
4) 146
5) 135
6) 138
7) 143
8) 148
9) 132
10)None of these

Solution

69
[69+(6+9)]+9 = (69+15)+9 = 84+9 = 93
[93+(9+3)]+3 = (93+12)+3 = 105+3 = 108
[108+(1+0+8)]+8 = (108+9)+8 = 117+8 = 125
Similarly
[125+(1+2+5)]+5 = (125+8)+5 = 133+5 = 138

Option 6)

Correct Option: 6 Best Solution (12)

17 Jun 2016 Diameter of sphere

Two metallic right circular cones having their height 4.1 cm and 4.3 cm and the radii of their bases 2.1 cm each, have been melted together and recast into a sphere. The diameter of the sphere is

OPtion

1) 4.2 cm
2) 4.8 cm
3) 2.5 cm
4) 1.4 cm
5) 1.8 cm
6) 3.9 cm
7) 3.5 cm
8) 5.8 cm
9) 6.3 cm
10)None of these

Solution

Sum of the volume of the cones = volume of the sphere
1/3*Pi*2.1^2*4.1 + 1/3*Pi*2.1^2*4.3 = 4/3*Pi*R^3
Solve
Diameter = 4.2 cm

Option 1)

Correct Option: 1 Best Solution (22)

16 Jun 2016 Base of the rectangle

If the base of a rectangle is increased by 10% and the area is unchanged, then the corresponding altitude must be decreased by:

OPtion

1) 100/11 %
2) 50/11 %
3) 10%
4) 4%
5) 11%
6) 13%
7) 100/9 %
8) 12%
9) 50/9 %
10)None of these

Solution

Let length = l and breadth = b.
Let, new breadth = x
Then, (110% of l)*x = lb
=> 110/100 lx = lb
x = 10/11 b
Decrease in breadth = [(b - 10/11 b)*1/b*100]% = 100/11 %

Option 1)

Correct Option: 1 Best Solution (29)