M4maths Previous Puzzles

18 May 2016 Coded language

If in coded language
SAURAV = SSUVSR
KRITIKA = TTRKRTK
ROHINI = IHOHOH
Then
RAKSHIT = ?

OPtion

1) RHRSSAI
2) SRHSAAI
3) RHKSITH
4) RRKHIST
5) ASTRRHI
6) KSRHITT
7) ARKSITH
8) SRSHRAI
9) ITRHAAR
10)RAISRSH

Solution

The position of letters of word SAURAV in English alphabet are 19, 1, 21, 18, 1, 22 respectively.
On writing the word SAURAV in a running sequence we get
SAURAVSAURAVSAURAVSAURAV.......
19th, 1st, 21st, 18th, 1st and 22nd letters in this sequence are S, S, S, U, V, S, R
Similarly for others

Option 8)

Correct Option: 8 Best Solution (5)

17 May 2016 Find the quantity of Milk

A mixture contains milk and water in the ratio 4:3. If 7 litres of water is added to it, the ratio of milk and water becomes 3:4. Find the quantity of milk in mixture.

OPtion

1) 8 litres
2) 10 litres
3) 12 litres
4) 17 litres
5) 13 litres
6) 14 litres
7) 15 litres
8) 16 litres
9) 11 litres
10)9 litres

Solution

Let milk = 4x and water = 3x
Then
4x / 3x+7 = 3/4
solve x = 3
Therefore
Milk = 4x = 12
Option 3)

Correct Option: 3 Best Solution (24)

16 May 2016 Sequence

What is the next number of the following sequence
12, 132, 1452, 15972, ..........

OPtion

1) 165792
2) 176592
3) 186592
4) 16961662
5) 16141692
6) 16149162
7) 16419162
8) 16146152
9) 156792
10)16146192

Solution

12
1 (1+2) 2 = 1 3 2 = 132
1 (1+3) (3+2) 2 = 1 4 5 2 = 1452
1 (1+4) (4+5) (5+2) 2 = 1 5 9 7 2 = 15972
Similarly
1 (1+5) (5+9) (9+7) (7+2) 2 = 1 6 14 16 9 2 = 16141692

Option 5)

Correct Option: 5 Best Solution (19)

13 May 2016 Number of ducks

Out of a group of ducks, 7/2 times the square root of the number are swimming in water while two remaining are playing on the shore. The total number of ducks is

OPtion

1) 2
2) 4
3) 6
4) 8
5) 10
6) 12
7) 14
8) 16
9) 18
10)None of these

Solution

Let the number of ducks be x.
Then, 7/2 sqrt(x) + 2 = x
=> 2x - 7 sqrt(x) - 4 = 0
=> (2y+1)(y-4) = 0
=> y = -1/2 or y = 4
=> sqrt(x) = -1/2 or sqrt(x) = 4
=> x = 1/4 or x = 16
Therefore
x=16 (Number of ducks can not be a fraction)
Option 8)

Correct Option: 8 Best Solution (6)

12 May 2016 Total income

5% of income of Swati is equal to 15% income of Raju and 10% income of Raju is equal to 20% income of Mohan. If income of Mohan is Rs.2000, then total income of Swati, Raju and Mohan (in rupees) is

OPtion

1) 5000
2) 4000
3) 6000
4) 8000
5) 9000
6) 14000
7) 12000
8) 16000
9) 18000
10)None of these

Solution

5/100 S = 15/100 R
and 10/100 R = 20/100 M
Therefore
S = (15/100 * 100/5)R = 3R
R = (20/100 * 100/10)M = 2M
Now M = 2000
R = 2*2000 = 4000
S = 3*4000 = 12000
12000+4000+2000 = 18000
Option 9)

Correct Option: 9 Best Solution (4)

11 May 2016 Number of person

A dinner party is to be fixed for a group consisting of 100 persons. In this party, 50 person do not prefer Veg, 60 prefer Non-veg and 10 do not prefer either Non-veg or Veg. The number of persons who prefer both Veg and Non-veg is

OPtion

1) 20
2) 35
3) 50
4) 55
5) 70
6) 60
7) 40
8) 30
9) 10
10)None of these

Solution

Let A be the set of persons who prefer Veg and B be the set of persons who prefer Non-veg.
Solve by using set theory
n(A U B) = 100 - 10 = 90
n(A) = 100 - 50 = 50
and n(B) = 60
Therefore
n(A Inter B) = n(A) + n(B) - n(A U B)
= 50+60 - 90) = 20
Ans - 20
Option 1)

Correct Option: 1 Best Solution (4)

10 May 2016 Stock

Ramesh invests some money partly in 3% stock at 96 and partly in 4% stock at 120. To get equal dividends from both, he must invest the
money in the ratio.

OPtion

1) 2:3
2) 16:15
3) 3:4
4) 3:5
5) 4:5
6) 3:4
7) 12:13
8) 4:7
9) 9:10
10)None of these

Solution

For an income of Rs.1 in 3% stock, investment
= Rs.(96/3) = Rs.32
For an income of Rs.1 in 4% stock investment
= Rs.(120/4) = 30
Ratio of investment = 32:30 = 16:15
Option 2)

Correct Option: 2 Best Solution (7)

09 May 2016 Sequence

What is the next number of the following sequence
59, 68, 74, 78, 85,......

OPtion

1) 91
2) 89
3) 92
4) 93
5) 97
6) 102
7) 104
8) 99
9) 101
10)None of these

Solution

59
5(9)+9 = 68 (Add last digit)
(6)8+6 = 74 (Add first digit)
7(4)+4 = 78 (Add last digit)
(7)8+7 = 85 (Add first digit)
Similarly
8(5)+5 = 90 (Add last digit)
Option 10)

Correct Option: 10 Best Solution (10)

06 May 2016 The correct root of the equation

Ramesh and Mohan solved a quadratic equation. In solving it, Ramesh made a mistake in the constant term and obtained the roots as 5,-3 while Mohan made a mistake in the coefficient of x and obtained the root as 1,-3. The correct root of the equation are

OPtion

1) 5,-3
2) -5,-3
3) 5,3
4) 5,-1
5) 1,-3
6) -1,-1
7) 1,-1
8) -1,-3
9) -1,3
10)+1,+3

Solution

Sum of root = 5+(-3) = 2
Product of root = 1*(-3) = -3
Therefore equation
x^2 - 2x - 3 = 0
(x-3)(x+1)=0
x=3, x=-1
Option 9)

Correct Option: 9 Best Solution (1)

05 May 2016 Linear Equations

A and B are two linear equation in two variable x and y. (0,1) is a solution of both A and B, (2,-1) is a solution of A only and (-2,-1) is a solution of B only. A and B are.

OPtion

1) x=0, y=1
2) x=0, x-y=-1
3) x+2y=2, 4x+y=1
4) 2x-y=-1, x-y=-1
5) x+y=1, x-y=-1
6) x+2y=2, x-y=-1
7) 2x-y=-1, 4x+y=1
8) x+y=1, x-y=-2
9) 2x-y=1, x-y=-1
10)x+2y=2, x+y=1

Solution

Let A and B be the equations given by ax+by=c and lx+my=n
Since (0,1) satisfies these equations, we have b=c and m=n
Since (2-1) satisfies ax+by=c, we have 2a-b=c
Therefore
2a-b=b or a=b (c=b)
Again
(-2,-1) satisfies lx+my=n we have -2l-m=d
or -2l-m=m or l=-m
Thus a=b=c and l=-m=-n
So the equation are
x+y=1 and x-y=-1
option 5)

Correct Option: 5 Best Solution (4)