M4maths Previous Puzzles

07 Jan 2010 Find the minimum value?

Minimum value of sum of a number and its square is ?
(Only real numbers are allowed)

OPtion

1) -1/4
2) -1/2
3) 0
4) 1/2
5) 1/4
6) 6
7) 2
8) -1/3
9) -1
10) 1

Solution

x + x2
= x + x2 +1/4 -1/4
= (x+1/2)2 -1/4
On taking x = -1/2, we get the minimum value of x + x2 as -1/4

Correct Option: 1 Best Solution (5)

06 Jan 2010 Profit?

Rahim got 12 & 1/4 dozen T-shirts in 12 % discount to printed price and he sold two third of
these T-shirts in 19 % profit to printed price, then he sold other T-shirts in printed price.
If his overall profit is 3626 rupee then printed price of the T-shirt is

OPtion

1) 95
2) 108
3) 94
4) 125
5) 136
6) 101
7) 100
8) 98
9) 84
10) 75

Solution

Let the printed price of the T-shirt is x, then according to given condition
1.19 x * 2/3 (147) + x * 1/3 (147) – 0.88 x *(147) = 3626
On solving this equation, we get x= 100

Correct Option: 7 Best Solution (3)

05 Jan 2010 red and black ball

A bag contains 6 black and 8 red balls. A ball is drawn at random from the bag. If the ball drawn is black, a coin is tossed twice otherwise no coin is tossed. What is the probability to get two heads respectively on the coins.

OPtion

1) 1/8
2) 1/4
3) 3/7
4) 1/7
5) 3/28
6) 3/14
7) 2/7
8) 1/2
9) 1/3
10) 1/48

Solution

Probability of drawing a black ball is 6/14 = 3/7
After then the probability of getting two successive heads is 1/2 * 1/2 = 1/4
Net probability = 3/7 * 1/4 = 3/28

Correct Option: 5 Best Solution (2)

04 Jan 2010 train speed?

Two trains A and B are moving in opposite direction in different tracks. The length of these trains are 100 m.
and 110 m. respectively. If speeds of A and B are in the ratio 4:5 and these two trains cross each other in 10 sec.
Then speed of train B is

OPtion

1) 70/3 m/s
2) 5/3 m/s
3) 50/9 m/s
4) 55/3 m/s
5) 35/3 m/s
6) 28/3 m/s
7) 4/3 m/s
8) 40/9 m/s
9) 84 m/s
10) 105 m/s

Solution

Let the speeds of the trains are 4v and 5v. Since the trains are moving in opposite direction,
relative speed of the train is 4v + 5v = 9v
According to the formula
speed = distance / time
9v = 210/10 = 21
or v = 7/3 hence speed of B is 5v = 5*7/3 = 35/3 m/s

Correct Option: 5 Best Solution (4)

01 Jan 2010 profit loss

Ram invests a sum of 8 lacs in two different businesses partly. In first business, he receives a profit of 3.5
lacs and in second business, he obtains a loss of 16 %. In overall business he obtains a profit of
40 %. The ratio of investments in first and second business is

OPtion

1) 44/5
2) 45/8
3) 42/3
4) 49/15
5) 40/3
6) 48/25
7) 36/5
8) 35/16
9) 1/2
10) 3/4

Solution

Let the investments in two businesses are respectively x & y
Then according to given conditions
x + 350000 + y × 0.84 = 1.4 (x + y) (i)
x + y = 800000 (ii)
On solving these two equations , we get x = 612500 and y = 187500

Correct Option: 4 Best Solution (3)

31 Dec 2009 How can I get this result?

If 12*7 = 103; 8*9 = 89; 7*11 = 95; then 6*13 is

OPtion

1) 96
2) 98
3) 99
4) 97
5) 95
6) 94
7) 93
8) 92
9) 91
10) 90

Solution

Here the formula used is a*b = a + b + (a × b)

Correct Option: 4 Best Solution (4)

30 Dec 2009 mark sheet printing mistake

Marks of Physics are printed in reverse order in the mark sheet of Surjeet. If printed marks are
less than the correct marks and he gets 67 % after this mistake then which % out of these options is
incorrect for the correct mark sheet (It is given that Surjeet gets success either according to
mark sheet obtained or according to corrected mark sheet. Total marks of the examination are 500)

OPtion

1) 74.2
2) 76.0
3) 70.6
4) 72.4
5) 79.6
6) 68.8
7) 77.8

Solution

In this reverse printing procedure possible conditions are as given below
Correct marks Printed marks Difference 43 34 9
53 35 18
54 45 9
63 36 27
64 46 18
65 56 9
73 37 36
74 47 27
75 57 18
76 67 9
83 38 45
84 48 36
85 58 27
86 68 18
87 78 9
93 39 54
94 49 45
95 59 36
96 69 27
97 79 18
98 89 9
Therefore possible increments in % are 1.8, 3.6, 5.4, 7.2, 9.0, 10.8
Hence the solution is 79.6 % with
increment of 12.6 %.

Correct Option: 5 Best Solution (1)

29 Dec 2009 Ratio and proportion

Amzad, Ali and Abbas start a shop with their investment ratio of 6:7:8. Amzad withdraws his investment after 2 month.
If profit is distributed between them yearly, then ratio of profit of Abbas and profit of Amzad in the business is -

OPtion

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

Solution

The effective proportion of Abbas = 8 × 12 (month) = 96
And the effective proportion of Amzad = 6 × 2 (month) = 12
Hence ratio is 96 : 12 = 8 : 1

Correct Option: 6 Best Solution (8)

28 Dec 2009 mango and orange

The cost (per Kg.) of mango and orange are between Rs 20 and 30. If total cost of 5 Kg mango and 7 Kg
orange is a number X having unit's and hundred's place equal and sum of cost of 1 Kg mango and 1 Kg
orange is Rs 50. Then the number X is

OPtion

1) 313
2) 282
3) 272
4) 333
5) 252
6) 303
7) 292
8) 323
9) 262
10) 343

Solution

There are 9 possibilities
No. Cost of mango/Kg. Cost of orange/Kg.
1 21 29
2 22 28
3 23 27
4 24 26
5 25 25
6 26 24
7 27 23
8 28 22
9 29 21
Check the following cases.

Correct Option: 7 Best Solution (5)

25 Dec 2009 decode the word

In a coded language
RATAN is written as PCRCL
PUJARI is written as NWHCPK
MADAN is written as KCBCL
SUPARI is written as QWNCPK
Then MADARI is written as .....

OPtion

1) KCBCPK
2) OYFYTG
3) KCBCOK
4) OYEYTG
5) LBCBQJ
6) LBCBPJ
7) LCBCPJ
8) KCFCPK
9) OYFYTH
10) JCBCPK

Solution

On taking the pattern of (x-2), (x+2), (x-2), (x+2)..... in the given words we can obtain the coded words.
In MADARI , on taking the given procedure we get KCBCPK

Correct Option: 1 Best Solution (0)