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Let Ronit's present age be x years. Then, father's present age =(x + 3x) years = 4x years.

	(4x + 8) =	5	(x + 8)
		2

8x + 16 = 5x + 40

3x = 24

x = 8.

Hence, required ratio =	(4x + 16)	=	48	= 2.
	(x + 16)		24

Given that:

1. The difference of age b/w R and Q = The difference of age b/w Q and T.

2. Sum of age of R and T is 50 i.e. (R + T) = 50.

Question: R - Q = ?.

Explanation:

R - Q = Q - T

(R + T) = 2Q

Now given that, (R + T) = 50

So, 50 = 2Q and therefore Q = 25.

Question is (R - Q) = ?

Here we know the value(age) of Q (25), but we don't know the age of R.

Therefore, (R-Q) cannot be determined.

100 years contain 5 odd days.

Last day of 1^st century is Friday.

200 years contain (5 x 2) 3 odd days.

Last day of 2^nd century is Wednesday.

300 years contain (5 x 3) = 15 1 odd day.

Last day of 3^rd century is Monday.

400 years contain 0 odd day.

Last day of 4^th century is Sunday.

This cycle is repeated.

Last day of a century cannot be Tuesday or Thursday or Saturday.

Let the average age of the whole team by x years.

11x - (26 + 29) = 9(x -1)

11x - 9x = 46

2x = 46

x = 23.

So, average age of the team is 23 years.

L.C.M. of 2, 4, 6, 8, 10, 12 is 120.

So, the bells will toll together after every 120 seconds(2 minutes).

In 30 minutes, they will toll together	30	+ 1 = 16 times.
	2

29.94	=	299.4
1.45		14.5

=		2994	x	1		[ Here, Substitute 172 in the place of 2994/14.5 ]
		14.5		10

=	172
	10

= 17.2

Go on multiplying the given numbers by 2, 3, 4, 5, 6.

So, the correct next number is 1440.

P.W. = Rs. (2562 - 122) = Rs. 2440.

S.I. on Rs. 2440 for 4 months is Rs. 122.

Rate =		100 x 122	%	= 15%.
		2440 x 1 3

  I. Material cost = Rs. 2.50 per m²

 II. Labour cost = Rs. 3500.

III. Total cost = Rs. 14,500.

Let the area be A sq. metres.

Material cost = Rs. (14500 - 3500) = Rs. 11,000.

	5A	= 11000     A =		11000 x 2		= 4400 m2.
	2			5

Thus, all I, II and III are needed to get the answer.

Correct answer is (C).

Go on adding 7, 9, 11, 13, 15, 17, 19 respectively to obtain the next number.

So, 135 is wrong.

Formula: If A can do a piece of work in n days, then A's 1 day's work =	1	.
	n

(A + B + C)'s 1 day's work =		1	+	1	+	1		=	7	.
		24		6		12			24

Formula: If A's 1 day's work =	1	,	then A can finish the work in n days.
	n

So, all the three together will complete the job in		24	days	=	3	3	days.
		7				7

Let 1 man's 1 day's work = x and 1 woman's 1 day's work = y.

Then, 4x + 6y =	1	and 3x + 7y =	1	.
	8		10

Solving the two equations, we get: x =	11	, y =	1
	400		400

1 woman's 1 day's work =	1	.
	400

10 women's 1 day's work =		1	x 10		=	1	.
		400				40

Hence, 10 women will complete the work in 40 days.

Ratio of rates of working of A and B = 2 : 1.

So, ratio of times taken = 1 : 2.

B's 1 day's work =	1	.
	12

A's 1 day's work =	1	; (2 times of B's work)
	6

(A + B)'s 1 day's work =		1	+	1		=	3	=	1	.
		6		12			12		4

So, A and B together can finish the work in 4 days.

The differences between two successive terms from the beginning are 7, 5, 7, 5, 7, 5.

So, 40 is wrong.

For managing, A received = 5% of Rs. 7400 = Rs. 370.

Balance = Rs. (7400 - 370) = Rs. 7030.

Ratio of their investments = (6500 x 6) : (8400 x 5) : (10000 x 3)

   = 39000 : 42000 : 30000

   = 13 : 14 : 10

B's share = Rs.		7030 x	14		= Rs. 2660.
			37

Let the number be x.

Then, x + 17 =	60
	x

x² + 17x - 60 = 0

(x + 20)(x - 3) = 0

x = 3.

Suppose the can initially contains 7x and 5x of mixtures A and B respectively.

Quantity of A in mixture left =		7x -	7	x 9		litres =		7x -	21	litres.
			12						4

Quantity of B in mixture left =		5x -	5	x 9		litres =		5x -	15	litres.
			12						4

	7x - 21 4	=	7
	5x - 15  + 9 4		9

	28x - 21	=	7
	20x + 21		9

252x - 189 = 140x + 147

112x = 336

x = 3.

So, the can contained 21 litres of A.

Since first and second varieties are mixed in equal proportions.

So, their average price = Rs.		126 + 135		= Rs. 130.50
		2

So, the mixture is formed by mixing two varieties, one at Rs. 130.50 per kg and the other at say, Rs. x per kg in the ratio 2 : 2, i.e., 1 : 1. We have to find x.

By the rule of alligation, we have:

Cost of 1 kg of 1st kind Cost of 1 kg tea of 2nd kind
Rs. 130.50	Mean Price Rs. 153	Rs. x
(x - 153)		22.50

	x - 153	= 1
	22.50

x - 153 = 22.50

x = 175.50

In the word 'CORPORATION', we treat the vowels OOAIO as one letter.

Thus, we have CRPRTN (OOAIO).

This has 7 (6 + 1) letters of which R occurs 2 times and the rest are different.

Number of ways arranging these letters =	7!	= 2520.
	2!

Now, 5 vowels in which O occurs 3 times and the rest are different, can be arranged

in	5!	= 20 ways.
	3!

Required number of ways = (2520 x 20) = 50400.

The word 'LEADING' has 7 different letters.

When the vowels EAI are always together, they can be supposed to form one letter.

Then, we have to arrange the letters LNDG (EAI).

Now, 5 (4 + 1 = 5) letters can be arranged in 5! = 120 ways.

The vowels (EAI) can be arranged among themselves in 3! = 6 ways.

Required number of ways = (120 x 6) = 720.