34. An error 2% in excess is made while measuring the side of a square. The percentage of error in the calculated area of the square is ?

Answer: 4.04%

Explanation:

100 cm is read as 102 cm.

 A₁ = (100 x 100) cm² and A₂ (102 x 102) cm².

(A₂ - A₁) = [(102)² - (100)²]

= (102 + 100) x (102 - 100)

= 404 cm².

Percentage error =		404	x 100	%	= 4.04%
		100 x 100

33. A and B can do a work in 8 days, B and C can do the same work in 12 days. A, B and C together can finish it in 6 days. A and C together will do it in :

Answer: 8 days

Explanation:

(A + B + C)'s 1 day's work =	1	;
	6

(A + B)'s 1 day's work =	1	;
	8

(B + C)'s 1 day's work =	1	.
	12

(A + C)'s 1 day's work	= 2 x 1 - 1 + 1 6 8 12
	= 1 - 5 3 24
	= 3 24
	= 1 . 8

So, A and C together will do the work in 8 days.

32. Student A has secured 9 marks more than student B and A's marks was 56% of the sum of A&B's marks. The marks obtained by A and B are??

Answer: 

42,33

Explanation:

Let their marks be (x + 9) and x.

Then, x + 9 =	56	(x + 9 + x)
	100

 25(x + 9) = 14(2x + 9)

 3x = 99

 x = 33

So, their marks are 42 and 33.

31. Find the missing number in 16, 33, 65, 131, 261, _____

Answer: 523

Explanation:

Each number is twice the preceding one with 1 added or subtracted alternatively.

So, the next number is (2 x 261 + 1) = 523.

30. A man on tour travels first 160 km at 64 km/hr and the next 160 km at 80 km/hr. The average speed for the first 320 km of the tour is ?

Ans : 71.11 km/hr

Explanation:

Total time taken =		160	+	160	hrs.	=	9	hrs.
		64		80			2

Average speed =		320 x	2	km/hr	= 71.11 km/hr.
			9

27. In how many ways can the letters of the word 'LEADER' be arranged?

Ans : 360


Explanation :

The word 'LEADER' contains 6 letters, namely 1L, 2E, 1A, 1D and 1R.

Required number of ways =	6!	= 360.
	(1!)(2!)(1!)(1!)(1!)

26. If a - b = 3 and a^2 + b^2 = 29, find the value of ab.

Ans :10

Explanation:
2ab = (a² + b²) - (a - b)²
   = 29 - 9 = 20
   ab = 10.

25. In how many ways can a group of 5 men and 2 women be made out of a total of 7 men and 3 women?

Answer: 63

Explanation:

Required number of ways = (7C5 x 3C2) = (7C2 x 3C1) =		7 x 6	x 3		= 63.
		2 x 1

23. A triangle is made from a rope. The sides of the triangle are 25 cm, 11 cm and 31 cm. What will be the area of the square made from the same rope?

Solution: 

Add all sides 25+11+31 to get rope length rope length =67,rope is made in to as square. So side of square is 67/4=16.75 and so area is 16.75*16.75=280.5625.
Ans : 280.5625

21. Four different integers are in increasing AP such that one number is equal to sum of the squares of the other three numbers.

Ans : 1,0,1,2

20. Rs 1,050 are divided among P, Q and R. The share of P is 2/5 of the combined share of Q and R. P gets ?

Ans : Rs 300

19. A train 130 metres long and travelling at 45 km/hr can cross a bridge in 30 seconds. Find the length of the bridge.

Answer:

245 m.  

Explanation:

Speed =		45 x	5	m/sec	=		25	m/sec.
			18				2

Time = 30 sec.

Let the length of bridge be x metres.

Then,	130 + x	=	25
	30		2

 2(130 + x) = 750

 x = 245 m.

17. The angle of elevation of the sun, when the length of the shadow of a tree 3 times the height of the tree, is??

Answer:
30º

Explanation:

Let AB be the tree and AC be its shadow.

Let ACB = .

Then,	AC	=	3          cot  = 3
	AB

  = 30º.

14. The sum of a positive number and its reciprocal is thrice d difference of d number and its reciprocal. Find d number?

Answer:
√2 (Root 2)

13. Total monthly salary of 4men and 2women is 46,000. If woman earn 500 more than man, then the salary of woman??

Answer:
Rs. 8000
Explanation:
Let x be salary of man.
y be salary of woman.
Then,
4x+2y=46000
x=y-500.
By solving above 2 equations we get y=8000

12. Find the speed of the 2nd train.

A train 108m long moving at a speed of 50km/hr crosses a train 112m long coming from opposite direction in 6sec.The speed of the 2nd train is??


Answer:
82 km/hr

Explanation:

Let the speed of the second train be x km/hr.

Relative speed	= (x + 50) km/hr
	= (x + 50) x 5 m/sec 18
	= 250 + 5x m/sec. 18

Distance covered = (108 + 112) = 220 m.

	220	= 6
	250 + 5x 18

 250 + 5x = 660

 x = 82 km/hr.

10. What is the age of the youngest child?

The sum of the ages of 5 children born at the interval of 3 years each is 50 years. What is the age of the youngest child?

Answer: 
4 years.

Explanation:
Let the ages of the children be x, (x + 3), (x + 6), (x + 9) and (x + 12) years.
Then, x + (x + 3) + (x + 6) + (x + 9) + (x + 12) = 50
     =>5x = 20
     =>x = 4.
Therefore, Age of the youngest child = x = 4 years.

9. Find the number.

When 75% of a number is added to 75, it results in the number itself. Find the number?

Answer:
300
Explanation:

Let the number be ‘x’. 75% of x can be written as 3/4x.

Given, 3/4x+75=x

Solving gives x=300.

7. Find the length of the wire.

A copper sphere of diameter 9 cm is melted and drawn into a wire of 2 mm diameter. The length of the wire is???

Answer:  
1093.5 mm or 1.1m (approx)
Explanation:
Volume of Sphere = Volume of wire(cylinder)
4(pi*R^3)/3 = pi*r^2*h
R=4.5 & r=1mm
h=1093.5 mm or 1.1m(approx)

3. What's the man's age?

A man is three times as old as his son. Five years later he will be two and a half times as old as his son.What's the man's age?

Answer: 
Age of the man = 45
Explanation:
Let the age of son & father be x & 3x.
After 5 yrs
son=x+5
father=3x+5
Also given,
2.5(x+5)=3x+5,
solving gives x=15.
fathers age=3x=45