Answer : D

Explanation

Let the present ages of the man his son be 11x and 5x respectively.
According to the question,
11x + 5x = 2*48
Or, 16x = 96
Or, x = 6

Therefore, present age of the man = (11*6)  = 66 years
Present age of the son = (5*6)  = 30 years

Hence required ration after 6 years = (66+6) : (30+6)
= 72 : 36
= 2:1

Answer : A

Explanation

Total age of remaining 40 girls = (80*20 - 20*22 ? 20*24)
= (1600-440-480)
= 680 years
Therefore average age for the 40 girls = 680/40 = 17 years

Answer : C

Explanation

Let the present ages of Arzoo and Arnav be 11x and 13x respectively.
According to the question,
(11x + 7) / (13x + 7) = 20/23
Or, 26x + 140 = 253x + 161
Or, 260x - 253x = 161 - 140
Or, 7x = 21
Or, x =  3

Difference between  their ages = 13x - 11x
= 2x
= 2*3
=  6 years

Answer : C

Explanation

Ram : Mohan = 4:5
Mohan : Anil = 5:6
Ram : Mohan : Anil = 4:5:6
Therefore, Mohan?s age = (5/15) * 90 = 30 years

Answer : C

Explanation

Supervisor?s age = 32 + 6 = 38 years

Answer : B

Explanation

Total age decreased = 24 * 1 months = 24 months or 2 years.
Therefore, age of the new comer = 18 ? 2 = 16 years

Answer : D

Explanation

The age of the daughter = (3*28) - (2*38)
= 84 - 76
=  8 years

Answer : D

Explanation

Count the number of odd days from the year 2007 onwards,
to get the sum equal to 0 odd days.

years
2007
2008
2009
2010
2011
2012
2013
2014
2015
2016
2017
Odd Days
1
2
1
1
1
2
1
1
1
2
1

Sum =14 odd days=0 odd day.
∴ Calendar for the year 2018 will be the same as for the year 2007.

Answer : D

Explanation

We might discover the day on first April, 2001.
First April , 2001=(2000 year + Period structure 1.1.2001 to 1.4.2001)
Odd days in 1600 years =0.
Odd days in 400 year =0.

Jan Feb March April
31 + 28 + 31 + 1 = 91 days =0 odd day.

Aggregate number of odd days= (0+0+0) =0.

On first April, 2001 it was Sunday.
In April, 2001 Wednesday falls on 4th, 11th, 18th and 25th.

Answer : D

Explanation

17th June, 1998= (1997 year Period structure 1.1.1998 to 17.6.1998)
Odd days in 1600 year=0.
Odd days in 300 year = (5*3) =1.
97 year has 24 jump year +73 standard years.
= 24*2 + 73*1
= 48 + 73
= 121 odd days
= 17 weeks + 2 odd days = 2 odd days
= 2 odd days.
∴ 1998 years have (0+1+2) = 3 odd days

Jan to June = (31+29+31+30+31)
= 152 days

Add 17 days of June.
= 152 + 17
= 169 days
= 24 weeks + 1 days
= 1 odd day.

∴ Total number of odd day = 3 + 1 = 4 odd days.
Hence 17.06.1998 was Thursday.

Answer : D

Explanation

28.May,2006 =(2005 years +Period structure 1.1.2006 to 28.5.2006)
Odd days in 1600 years=0.
Odd days in 400 years = 0.

5 years = (4 common years+ 1 jump years)=(4*1+1*2)odd days
= 6 odd days.

Jan + Feb. + March + April + May
31 + 28 + 31 + 30 + 28 =148 days.

148 days = (21 weeks+1 day) = 1 odd day
Aggregate no. of odd days = (0+0+6+1) = 7= 0 odd day.
 
Given day is Sunday.

Answer : A

Explanation

fifteenth August,2010 =(2009 years+ Period from 1.1.2010 to 15.8.2010)
Odd days in 1600 years = 0.
Odd days in 400 years = 0.

9 year = (2 jump year +7 conventional years)
= (2*2+7*1) = 11 odd days= 4 odd days

Jan + feb + March + April + May + June + July + august
31+28+31+30+31+30+31+15 = 227 days =(32 weeks +3 days )
= 3 odd days

Aggregate no. of odd days = (0+0+4+3) =7
= 0 odd day

Given day is Sunday.

Answer : B

Explanation

Each day of the week is rehashed following 7 days.
In this way, after 63 days it will be Monday.
∴ Following 61 days , it will be Saturday.

Answer : C

Explanation

100 years contain 5 odd days.
∴ Last day of first century is Friday. 

200 years contain (5*2) = 3 odd days.
∴ Last day of second century is Wednesday.

300 year contain (5*3) =15=1 odd day.
∴ Last day of third century is Monday.

400 year contain 0 odd days.
∴ Last day of fourth century is Sunday.

The cycle is repeated.
∴ Last day of a century can't be Tuesday or Thursday or Saturday.

Answer : A

Explanation

The century divisible by 400 is a leap year.
∴ The year 700 is not a jump year.

Answer : B

Explanation

Speed downstream = (5+1) km/hr=6 km/hr`Speed upstream = (5-1) km/hr=4 km/hr.`Let the required distance be x km. Then,`x/6+ x/4=75/60 = 5/4 => (2x+3x) =15 => 5x = 15 => x=3.`Required distance =3km.

Answer : A

Explanation

Speed upstream =3/3 km/hr =1 km/hr.`Speed downstream =15/3 km/hr=5 km/hr.`Speed of current =1/2 (5-1) km/hr =2 km/hr

Answer : C

Explanation

Let the speed of boat be x km /hr and speed of stream be y km/hr.`44/5 * (x-y) = 4 * (x+y) => 44(x-y) =20 (x+y) => 11 (x-y) = 5(x+y) => 6x=16y`=> x/y= 16/6 = 8/3 => x: y = 8:3.

Answer : C

Explanation

Speed in still water =6 km/hr.`Speed against the current =6/3 km/hr =2 km/hr`Let the speed of the current be x km/hr`6-x = 2 => x = 4 km/hr.

Answer : B

Explanation

Let the speed of the steamer in still water be x km/hr.`Speed downstream = (x +2) km/hr, speed upstream = (x-2) km/hr.`Then 4 (x+2) = 5 (x-2) => x = 18.`Hence, the speed of the streamer in still water is 18 km/hr.

Answer : C

Explanation

Let the speed of the boat in still water be x km/hr and the speed of the stream be y km/hr.`Then, Speed upstream = (x-y) km/hr, Speed downstream = (x+y) km/hr`24/(x-y) + 28/ (x + y) = 6 => 24a + 28b = 6, where x-y = 1/a and x + y = 1/b`=>12a + 14 b = 3`30/ (x-y) + 21/ (x+y) = 13/2 => 60a + 42 b = 13`On solving (i) and (ii), we get: 28b =2 => b = 1/14 and a = 1/6`∴ (x-y=6 and x+y = 14) => x = 10, y=4.`Speed of the boat in still water=10 km/hr

Answer : C

Explanation

Upstream Speed of motor boat = 56/1 hr 45 min = 32 kmph`Speed of the motor boat in still water = 36 kmph`Speed of the boat in still water = 1/2*(Downstream Speed + Upstream Speed)`36 = 1/2(d + 32)`Downstream Speed (d) = 40 km/hr``t = Distance/speed = 40/36 = 7/5 hr = 1 hr 24 mins

Answer : B

Explanation

The given equations are
2x+ y=8...  (1)     4x-3y=-4 ...(2)
On multiplying (1) by 3 and adding (2) to it, we get:
 10x= 20
 ⇒x= 2
Putting x= 2 in (1), we get: 4+ y = 8   ⇒y = 4
∴ x= 2, y= 4

Answer : C

Explanation

The given equations are
9x+ 2y = 198...(i)
2x+y =54...(iii)
On multiplying (ii) by 2 and subtracting it from (i), we get: 5x= 90 ⇒x= 18
Putting x=18 in (ii), we get: 36+y = 54 ⇒y = 18
∴x = 18, y= 18

Answer : A

Explanation

Putting y = x+3 in 2x+3y = 29, we get :
2x+3 (x+3) = 29 ⇒5x = 20
 ⇒x= 4

Answer : C

Explanation

Given equations are 4/x+5 y= 7 ...(i)
3/x+4y = 5  ...(ii)
On multiplying (i) by 3, (ii) by 4 and subtracting, we get -y =1 ⇒y= -1
Putting y= -1 in (i), we get 4/x-5 = 7 ⇒4/x= 12 ⇒12x= 4 ⇒x= 1/3
∴x= 1/3, y= -1

Answer : A

Explanation

Clearly x= 5 and y= ℏ satisfies 2x+y- 6 = 0
∴ 2*5+ ℏ-6= 0 ⇒ 10+ℏ- 6= 0 ⇒ℏ+4= 0 ⇒ ℏ= -4

Answer : D

Explanation

Given 3x+7y = 75  ...(i)
5x-5 y= 25 ⇒x-y = 5...(ii)
Multiplying (ii) by 7 and adding to (i), we get:
10 x = 110   ⇒x = 11
Putting x = 11 in (ii), we get: y=(11-5) = 6
∴ x+y = (11+6) = 17

Answer : C

Explanation

Given equations are 3x+4y= 5 ...(i) and x+2y =2 ...(ii)
On multiplying (ii) by 3 and subtracting (i) from it, we get 2y = 1 ⇒y = 1/2
Putting y = 1/2 in (ii), we get x+2*1/2 = 2 ⇒x+1= 2 ⇒x =1
∴(x+y ) = (1+1/2 ) = 3/2

Answer : B

Explanation

Given equations are p/x+q/y = m...(i),   q/x+ p/y = n ...(ii)
On multiplying (i) by q, (ii) by p and subtracting, we get:
q2/y- p2/y = mq-np
⇒y (mp-np) = (q2- p2)
⇒y = (q2-p2)/(mq- np)
= (p2- q2)/(np-mq)
On multiplying (i) by p, (ii) by q and subtracting, we get:
p2/x - q2/x = mp- nq
⇒ (p2- q2) = x (mp- nq)
⇒x = (p2- q2)/ (mp-nq)
∴ x= (p2-q2)/(mp-nq) , y = (p2-q2)/(np- mq)

Answer - D

Explanation

Pass% in 2005 = (1500/1800*100)%= 250/3% = 83.33%

Answer - C

Explanation

Pass% in 2005    = (1500/1800*100)%= 83.33%
Pass % in  2006  = (1600/2000*100)%=80%
Pass % in 2007 = (1750/2050*100)% = 85.3%
∴ The collage had best result for B.sc in 2007.

Answer - B

Explanation

Number of 3rd divisions  in 2007 = (1750-1000)= 750

Answer - D

Explanation

Required % = (2050/1800*100)%  = 113.8%

Answer - B

Explanation

Required % =  { (1500+1600+1750)/(1800+2000+2050)*100} = (4850/5850*100)%  = 82.9%

Answer : A

Explanation

Payment to be made = P.W. of Rs. 10028 due 9 months hence
= Rs ((100*10028))/(100+(12*3/4) )= Rs ((100*10028))/109= Rs 9200

Answer : D

Explanation

P.W. of loan on A = Rs ((100*1573))/(100+(14*2/3) )= Rs ((100*1573))/121= Rs 1300
P.W. of loan on B = Rs ((100*1444.50))/(100+(14*1/2) )= Rs ((144450))/103= Rs 1350
So, B will pay Rs. 50

Answer : C

Explanation

Successive discount is calculated as X+Y-XY/100 %
Successive discount =15+16-15*16/100=31-240/100=28.6 %

Answer : B

Explanation

Let us assume cost price is 100.Then the marked price is 130
SP=130 * 80/100= 104.
Profit % =(S.P-C.P)/(C.P) * 100=(104-100)/100 * 100 
=4%

Answer : A

Explanation

Present worth=( 100*TD)/R*T=( 100 *180 )/10*3=Rs.600.

Answer : C

Explanation

Slop = (y₁ ?y₂)/( x₁-x₂) = (2+1)/ (3-3) = 3/0, which is not defined

Answer : A

Explanation

   (3-5)/x-2 =2 ⇒ 2x-4 =-2 ⇒ 2x =2 ⇒ x= 1

Answer : D

Explanation

Slop of AB = (5+3)/(2-x) =8/2-x
 ∴ 8/2-x = tan135⁰ = tan (180⁰- 45⁰) = -tan 45⁰ =-1 
8/2-x = -1 ⇒8 = x-2 ⇒ x= 10

Answer : B

Explanation

The equation of the line is (y-y₁)/(x-x₁) =
 (y₂-y₁)/(x₂-x₁)
 i.e., (y-1)/(x+1) = -4-1/2+1 ⇒ (y-1)/(x+1) = -5/3
 ⇒ 3y-3= -5x-5 ⇒ 5x+3y+2 = 0

Answer : A

Explanation

The equation of the line is:
 Y-5/x-3 = tan 135⁰ = tan (180⁰-45⁰) = -tan 45⁰ =-1
 ⇒ Y-5 =3-x = > x+y -8 = 0

Answer : C

Explanation

The equation of the line is y+4/x-3 = tan0= 0 ⇒ y+4 = 0

Answer : A

Explanation

Since the given lines are parallel, we have 1/ℏ =2/4 ⇒ ℏ = 2

Answer : C

Explanation

Angle traced by the hour hand in 12 hours = 360°
Angle traced by it 3 hr 25 minutes i.e 41/12 hrs
= 360°/12 * 41/12 = 105°/2
Similarly, angle traced by min hand in 60 mins = 360°
Angle traced by it in 25 mins = 3600/60 * 25 = 150°

∴ Angle between hour hand and minute hand
= 150° ? 105°/2
= 95°/2

Answer : A

Explanation

At 2 o' clock, the hour hand is at 2 and minute hand is at 12
i.e. they are 10 min spaces apart.
The minute hand has to gain 10 minute spaces
over the hour hand to be together.

The minute hand gains 55 mins in 60 mins.
∴ It will gain 10 mins in 60/55 * 10 min
= 120/11 minutes.

Hence the hands will coincide at 120/11 minutes past 2.

Answer : A

Explanation

At h o' clock, the minutes hand is 5 h minute spaces
behind the hour hand.
The minute hand gains 55 min spaces in 60 mins.

∴ The minute hand will gain 5h minute spaces
in 60/55 * 5h = 60h/11 minutes.

∴ The two hands will be together between
'h' and 'h+1' o' clock at (60/11)h minutes h o' clock.