Present ages of son and father be x years (56 -x)years

(56- x +4) = 3(x + 4) or 4x =48 or x = 12

Ages are 12 years, 44 years.

The ratio in which the four agencies will be paying the rents = 15 * 12 : 12 * 20 : 18 * 18 : 16 * 15

= 180 : 240 : 324 : 240 = 45 : 60 : 81 : 60

Let us consider the four amounts to be 45k, 60k, 81k and 60k respectively.

The total rent paid by the four agencies = 45k + 60k + 81k + 60k= 246k

It is given that A paid Rs. 1125

45k = 1125 => k = 25

246k = 246(25) = Rs. 6150

Thus the total rent paid by all the four agencies is Rs. 6150.

Let the price of the article = Rs.100

New price = 100 - 10 = 90

Therefore the new price must be increased by(100−90)×100/90=100/9%=11 1/9%.

Speed of train relative to man = 60 + 6 = 66 km/hr.

= 66 * 5/18 = 55/3 m/sec.

Time taken to pass the men = 110 * 3/55 = 6 sec.

Rita’s age 2 years ago be x years

Pushpa’s present age =(2x) years

2x –(x +2) =2 => x =4

Therefore pushpa’s present age = 8 years.

The ratio of their profits A:B = 8:12 = 2:3

Share of A in the total profit = 2/5 * 25000 = Rs.10000 Share of A in the total profit = 3/5 * 25000 = Rs.15000.

264, 396, 462, 792, 968, 2178, 5184, 6336

132 = 11 * 3 * 4

Clearly, 968 is not divisible by 3

None of 462 and 2178 is divisible by 4

And, 5284 is not divisible by 11

Each one of the remaining four numbers is divisible by each one of 4, 3 and 11.

So, there are 4 such numbers.

Ratio of investments of A and B is (70000 * 12) : (120000 * 6) = 7 : 6

Total profit = Rs. 52000

Share of B = 6/13 (52000) = Rs. 24000.

Given sum = 9 + 3/4 + 7 + 2/17 - (9 + 1/15)

= (9 + 7 - 9) + (3/4 + 2/17 - 1/15)

= 7 + (765 + 120 - 68)/1020 = 7 817/1020.

Ratio of investments of A, B and C is 8000 : 10000 : 12000 = 4 : 5 : 6

And also given that, profit share of B is Rs. 1500

=> 5 parts out of 15 parts is Rs. 1500

Now, required difference is 6 - 4 = 2 parts

Required difference = 2/5 (1500) = Rs. 600.

Interest received by A from B = 10% of half of Rs.50000 = 10% * 25000 = 2500.

Amount received by A per annum for being a working partner = 1500 * 12 = Rs.18000.

Let 'P' be the part of the remaining profit that A receives as his share. Total income of A = (2500 + 18000 + P)

Total income of B = only his share from the remaining profit = 'P', as A and B share the remaining profit equally.

Income of A = Twice the income of B

(2500 + 18000 + P) = 2(P)

P = 20500

Total profit = 2P + 18000

= 2*20500 + 18000 = 59000.

Time for one revolution = 60/15 = 4

60/ 20 = 3

60/48 = 5/4

LCM of 4, 3, 5/4

LCM of Numerators/HCF of Denominators =

60/1 = 60.

Length = 6x

Breadth = 5x

Height = 4x in cm

Therefore, 2(6x × 5x + 5x × 4x + 6x × 4x) = 33300

148x^{2} = 33300

=> x^{2} = 33300/148 = 225

=> x = 15.

Therefore, Length = 90cm,

Breadth = 75cm,

Height = 60cm

90, 75 , 60 cm.

Let the number be x. Then,

2/5 of 1/3 of 3/7 of

x = 15 => x = (15 * 5/3 * 3 * 5/2) = 525/2

40% of 525/2 = (40/100 * 525/2) = 105.

Let the length of the train be x m and its speed be y m/sec.

Then, x/y = 8 => x = 8y

(x + 264)/20 = y

y = 22

Speed = 22 m/sec = 22 * 18/5 = 79.2 km/hr.

Let the number be x. Then,

50% of x - 35% of x = 12

50/100 x - 35/100 x = 12

x = (12 * 100)/15 = 80.

The number of liters in each can = HCF of 80, 144 and 368 = 16 liters.

Number of c of Maaza = 80/16 = 5

Number of c of Pepsi = 144/16 = 9

Number of c of Sprite = 368/16 = 23

The total number of c required = 5 + 9 + 23 = 37 c.

A invests Rs.8000 for 18 months, but B invests Rs.8000 for the first 4 months and then withdraws Rs.4000.

So, the investment of B for remaining 14 months is Rs.4000 only.

A : B

8000*18 : (8000*4) + (4000*14)

14400 : 88000

A:B = 18:11.

Let original price = Rs. 100.

Reduced Price = Rs. 75.

Increase on Rs. 75 = Rs. 25

Increase on 100 = (25/75 x 100) % = 33 1/3 %.

Suppose, salary = Rs. 100

Expenditure on food = Rs. 40

Balance = Rs. 60

Expenditure on trport = 1/3 × Rs. 60 = Rs. 20

Now, balance = Rs. 40

Saving = Rs. 20

If saving is = Rs. 20

Salary = Rs. 100

If saving is Rs. 450,

salary = Rs (100/20 x 450) = Rs. 2250.

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.

Age of youngest child = x = 4 years.

Speed = 300/18 = 50/3 m/sec.

Let the length of the platform be x meters.

Then, (x + 300)/39 = 50/3

3x + 900 = 1950 => x = 350 m.

Lowest 4-digit number is 1000.

LCM of 3, 4 and 5 is 60.

Dividing 1000 by 60, we get the remainder 4@Thus, the lowest 4-digit number that exactly divisible by 3, 4 and 5 is 1000 + (60 - 40) = 1020.

Now, add the remainder 2 that's required. Thus, the wer is 1022.

Width of the carpet = 63/100 m let it’s length be x metres

Then x × 63/100 = 14 x 9

=> x =(14 x 9 x 100/63) = 200m

Length = 200m.

Length of the be let ‘l’ units and breadth be b units

Area =lb sq. Units

Now length =(110/100 l) = 11l/10

New breadth =(90/100 b) = 96/10

Now area (11l/10 x 96/10)Sq.units = (99/100 lb)sq.unit

Area decreased = (lb -99/100 lb)sq.units =lb/100 sq.Units

Percentage decreased =(lb/100 x 1/lb x 100)% = 1%.

15:25 => 3:5

9600*10/100 = 960

9600 - 960 = 8640

8640*3/8 = 3240 + 960

= 4200.

Let Rajan's present age be x years.

Then, his age at the time of marriage = (x - 8) years.

x = 6/5 (x - 8)

5x = 6x - 48 => x = 48

Rajan's sister's age at the time of his marriage = (x - 8) - 10 = 30 years.

Rajan's sister's present age = (30 + 8) = 38 years.

Let the business value changes from x to y.

Then 4 % of x = 5 % of y of 4/100 × x = 5/100 × y

or y = 4/5 x.

Change in business = (x - 4/5 x) = 4/5 x.

Percentage slump in business

= (1/5 x ×1/x × 100)% = 20%.

Speed of train relative to jogger = 45 - 9 = 36 km/hr.

= 36 * 5/18 = 10 m/sec.

Distance to be covered = 240 + 120 = 360 m.

Time taken = 360/10 = 36 sec.

(4 + 5 + 2) - (1 + 6 + 3) = 1, not divisible by 11.

(2 + 6 + 4) - (4 + 5 + 2) = 1, not divisible by 11.

(4 + 6 + 1) - (2 + 5 + 3) = 1, not divisible by 11.

(4 + 6 + 1) - (2 + 5 + 4) = 0.

So, 415624 is divisible by 11.

Let the length of the train be x m and its speed be y m/sec.

Then, x/y = 15 => y = x/15

(x + 100)/25 = x/15 => x = 150 m.

Let the number be x. Then,

x - 2/5 x = 510

x = (510 * 5)/3 = 850

10% of 850 = 85.

Length = 6 m 24 cm = 624 cm

Width = 4 m 32 cm = 432 cm

HCF of 624 and 432 = 48

Number of square tiles required = (624 * 432)/(48 * 48) = 13 * 9 = 117.

16.66% of 33.33% of 66.66% of x = 30

= 1/6 of 1/3 of 2/3 of x = 30

=> (30 * 6 * 3 * 3)/2 => x = 810

Speed downstream = 24/10 km/hr = 2.4 km/hr

Speed upstream = 24/12 km/hr = 2 km/hr

Speed of the boat in still water = ½ (2.4 +2)km/hr = 2.2 km/hr.

Speed = 54 * 5/18 = 15 m/sec.

Length of the train = 15 * 20 = 300 m.

Let the length of the platform be x m . Then,

(x + 300)/36 = 15 => x = 240 m.

6a^{2}= 726

=> a^{2} = 121

=> a = 11 Cm

Therefore, Volume of the cube

= (11 × 11 × 11) cm^{3} = 1331 cm^{3}.

**Calculate the differences, taking two numbers at a time as follows:**

(215-47) = 168

(365-215) = 150

(365-47) = 318

HCF of 168, 150 and 318 we get 6, which is the greatest number, which while dividing 47, 215 and 365 gives the same.

emainder in each cases is 5.

Let the speed of motor boat be 36x km/hr and that of current of water be 5x km/hr

Speed downstream = (36x +5x)km/hr = 41x km/hr

Speed upstream = (36 -5x)km/hr = 31x km/hr

Distance covered downstream = (41x × 31/6)km

Distance upstream = [1271x/6 × 1/31x]hrs

= 41/6 hrs = 6hrs 50 min.

Let length = 100 m.

Breath = 100 m.

New length = 160 m.

New breath = x meters

Then, = 160 × x = 100 × 100

(or) X = (100 ×100)/160 × 125/2

Decrease in breadth = (100- 125/2) % = 37 ½ %.

Let the number x. Then,

20% of x = 120

x = (120 * 100)/20 = 600

120% of x = (120/100 * 600) = 720.

Let the distance between the two parts be x km.

Then speed downstream = x/4 km/hr.

Speed Upstream = x/5 km/hr

Speed of the stream = ½ (x/4 –x/5)

Therefore, ½(x/4 –x/5) = @=> x/4 –x/5 = 4 => x = 80.

Hence, the distance between the two ports is 80km.

Let tax = Rs. 100 and consumption = 100 units

Original Expenditure = Rs. (100 × 100) = Rs. 10000

New Expenditure = Rs. (120 × 80) = Rs. 9600

Decrease in expenditure = (400/10000 x 100) % = 4 %.

Speed of train relative to man = 63 - 3 = 60 km/hr.

= 60 * 5/18 = 50/3 m/sec.

Time taken to pass the man = 500 * 3/50 = 30 sec.

Speed of the train relative to man = 125/10 = 25/2 m/sec.

= 25/2 * 18/5 = 45 km/hr

Let the speed of the train be x km/hr. Then, relative speed = (x - 5) km/hr.

x - 5 = 45 => x = 50 km/hr.

Let the numbers be a and b. Then,

a + b = 12 and ab = 35.

(a + b)/ab = 12/35

= (1/b + 1/a) = 12/35

Sum of reciprocals of given numbers = 12/35.

Mother's age when Ayesha's brother was born = 36 years.

Father's age when Ayesha's brother was born = (38 + 4) = 42 years.

Required difference = (42 - 36) = 6 years.

Relative speed = 60 + 40 = 100 km/hr.

= 100 * 5/18 = 250/9 m/sec.

Distance covered in crossing each other = 140 + 160 = 300 m.

Required time = 300 * 9/250 = 54/5 = 10.8 sec.

Let price = Rs. 100, Sale = 100

Then Sale Value = Rs. (100 × 100) = Rs. 10000

New Sale Value = Rs. (70 × 120) = Rs. 8400

Decrease % = (1000/10000 x 100) % = 16 %.

Ratio of investments of P and Q is 2 : 5

Total salary claimed by P = 12 * 5000 = Rs. 60000

Total profit = Rs. 2 lakhs.

Profit is to be shared = Rs. 140000

Share of P = (2/7) * 140000 = Rs. 400000

Share of Q = Rs. 100000

Total earnings of P = (60000 + 40000) = Rs. 100000

Ratio of their earnings = 1 : 1.