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Since the month begins with a Sunday, to there will be five Sundays in the month.

Required average	= 510 x 5 + 240 x 25 30
	= 8550 30
	= 285

Let the ages of Kunal and Sagar 6 years ago be 6x and 5x years respectively.

Then,	(6x + 6) + 4	=	11
	(5x + 6) + 4		10

10(6x + 10) = 11(5x + 10)

5x = 10

x = 2.

Sagar's present age = (5x + 6) = 16 years.

Let the ages of father and son 10 years ago be 3x and x years respectively.

Then, (3x + 10) + 10 = 2[(x + 10) + 10]

3x + 20 = 2x + 40

x = 20.

Required ratio = (3x + 10) : (x + 10) = 70 : 30 = 7 : 3.

Angle traced by hour hand in	21	hrs =		360	x	21		°	=	157	1	°
	4			12		4					2

Angle traced by min. hand in 15 min. =		360	x 15		°	= 90°.
		60

Required angle =		157	1		°	- 90° = 67	1	°
			2				2

log₁₀ 5 + log₁₀ (5x + 1) = log₁₀ (x + 5) + 1

log₁₀ 5 + log₁₀ (5x + 1) = log₁₀ (x + 5) + log₁₀ 10

log₁₀ [5 (5x + 1)] = log₁₀ [10(x + 5)]

5(5x + 1) = 10(x + 5)

5x + 1 = 2x + 10

3x = 9

x = 3.

A : B = 100 : 80.

A : C = 100 : 72.

B

=

B

x

A

=

80

x

100

=

10

=

100

= 100 : 90.

C

A

C

100

72

9

90

B can give C 10 points.

C.I.	= Rs. 4000 x 1 + 10 2 - 4000 100
	= Rs. 4000 x 11 x 11 - 4000 10 10
	= Rs. 840.

Sum = Rs.		420 x 100		= Rs. 1750.
		3 x 8

Let C.P. be Rs. x.

Then,	1920 - x	x 100 =	x - 1280	x 100
	x		x

1920 - x = x - 1280

2x = 3200

x = 1600

Required S.P. = 125% of Rs. 1600 = Rs.		125	x 1600		= Rs 2000.
		100

Video Explanation: https://youtu.be/0tTd5TwCspY

For an income of Re. 1 in 9% stock at 96, investment = Rs.		96		= Rs.	32
		9			3

For an income Re. 1 in 12% stock at 120, investment = Rs.		120		= Rs. 10.
		12

Ratio of investments =	32	: 10 = 32 : 30 = 16 : 15.
	3

Let there be x children.

I gives, age of teacher = x years.

II gives, average age of (x + 1) persons = (x + 1) years.

Teacher's age = (x + 1) (x + 1) - x² = (x² + 1 + 2x) - x² = (1 + 2x)

Thus, teacher's age cannot be obtained.

Correct answer is (D)

Let the original rate be R%. Then, new rate = (2R)%.

Note:
Here, original rate is for 1 year(s); the new rate is for only 4 months i.e. year(s).

		725 x R x 1		+		362.50 x 2R x 1		= 33.50
		100				100 x 3

(2175 + 725) R = 33.50 x 100 x 3

(2175 + 725) R = 10050

(2900)R = 10050

R =	10050	= 3.46
	2900

Original rate = 3.46%

L.C.M. of 252, 308 and 198 = 2772.

So, A, B and C will again meet at the starting point in 2772 sec. i.e., 46 min. 12 sec.

99 = 1 x 3 x 3 x 11

101 = 1 x 101

176 = 1 x 2 x 2 x 2 x 2 x 11

182 = 1 x 2 x 7 x 13

So, divisors of 99 are 1, 3, 9, 11, 33, .99

Divisors of 101 are 1 and 101

Divisors of 176 are 1, 2, 4, 8, 11, 16, 22, 44, 88 and 176

Divisors of 182 are 1, 2, 7, 13, 14, 26, 91 and 182.

Hence, 176 has the most number of divisors.

Given numbers are 1.08, 0.36 and 0.90.   H.C.F. of 108, 36 and 90 is 18,

H.C.F. of given numbers = 0.18.

Let the slower pipe alone fill the tank in x minutes.

Then, faster pipe will fill it in	x	minutes.
	3

	1	+	3	=	1
	x		x		36

	4	=	1
	x		36

x = 144 min.

Let (25)^7.5 x (5)^2.5 ÷ (125)^1.5 = 5^x.

Then,	(52)7.5 x (5)2.5	= 5x
	(53)1.5

	5(2 x 7.5) x 52.5	= 5x
	5(3 x 1.5)

	515 x 52.5	= 5x
	54.5

5^x = 5^{(15 + 2.5 - 4.5)}

5^x = 5¹³

x = 13.

Suppose originally he had x apples.

Then, (100 - 40)% of x = 420.

	60	x x = 420
	100

x =		420 x 100	= 700.
		60

Video Explanation: https://youtu.be/-Pv25Do3WwY

Le the required time be x seconds.

More metres, More time (Direct Proportion)

0.128 : 25 :: 1 : x       0.128x = 25 x 1

x =	25	=	25 x 1000
	0.128		128

x = 195.31.

Required time = 195 sec (approximately).

Let Principal = Rs. P and Rate = R% p.a. Then,

Amount = Rs.		P		1 +	R		4
					100

C.I. =	P			1 +	R		4	- 1
					100

	P			1 +	R		4	- 1		= 1491.
					100

Clearly, it does not give the answer.

Correct answer is (D).

Each number is a composite number except 11.